Official Soldat Forums
Misc => The Lounge => Topic started by: Camping_carl on November 05, 2006, 09:53:59 am
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does .99999999999 infinity = 1
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does .99999999999 infinity = 1
Haven't I seen this topic somewhere?
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yes i have started it on the lue but still have not got a intelligent answer.
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No. even though it goes on for infinity it never reaches an absolute 1. Unless you round up, but that defeats the whole purpose.
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This topic was posted before I sware.
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Probably in the past, does it really matter? If it was posted Carl will get an answer, then it will be locked. If not people will argue here until someone gets tired of argueing.
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Probably in the past, does it really matter?
Only to prove I'm not crazy.
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SHUTS UP just round to one for gods sake. The reason all of our maths is screwed is because the stupid guy that invented our number system made it like it is today, which causes problems with things like .999 and infinity. If only they had done it properly and thought about it before screwing it all up and making it impossible to calculate certain things >:(
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.99999 infinity approaches 1 but never gets there. I think its awesome. Approaching something but never ever getting there.
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Technically 0.9 recurring + 0.1 recurring = 1
However when doing maths it is acceptable to write 0.9 recurring = 1
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I think its awesome. Approaching something but never ever getting there.
Story of my life :P
Oh yeah, and CC you STILL DIDN'T announce the winner of the sig competition ?????????
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Without rounding up, 0.99~ is equal to one. You see, all integer numbers can be written in two ways, lets take 1 for example:
1.00000~
0.9999~
Em, remember how to turn numbers with infinite periodic decimals into fractions?
0.444444~ = 4/9
0.323232~ = 32/99
Well, do that with 0.9999~
0.9999999~ = 9/9 = 1
No need to know and understand the idea of limit, just read the explanation above.
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Without rounding up, 0.99~ is equal to one. You see, all integer numbers can be written in two ways, lets take 1 for example:
1.00000~
0.9999~
Em, remember how to turn numbers with infinite periodic decimals into fractions?
0.444444~ = 4/9
0.323232~ = 32/99
Well, do that with 0.9999~
0.9999999~ = 9/9 = 1
No need to know and understand the idea of limit, just read the explanation above.
Bloody educated nerd....:P
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I've seen people try to prove this via math on other forums where the same subject sprung up. I've also seen people successfully prove that 1 = 2. Hint, hint? ;)
It's like trying to get to "tomorrow" without a time-machine.
@Syd's post:
why the heck is 0.44-- = 4/9?! That should be 4/10 ???
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Technically 0.9 recurring + 0.1 recurring = 1
However when doing maths it is acceptable to write 0.9 recurring = 1
That's incorrect. 0.999~ + 0.111~ does not equal 1. However, 0.999~ + 0.00~1 does. The reason that this is such an issue in mathematics is the difference in significance of 0.999~ in graphs and integers. You see, in a graph, 0.999~ would be considered an asymptote; a function approaches either x = 1 or y = 1 but never really gets there. However, when dealing with integers and rational numbers, the method used would be the one that Syd gave above, especially because a rational number is any number that can be written as a fraction of integers, and an integer itself is classified as a rational number. ;D
Edit: In response to Keron's post:
No, 0.4 would equal 4/10. There is a mathematical theorem that states that 0.x~ = x/9 and 0.xyxy~ = xy/99, and so on. The numbers after the decimal that repeat are given as a fraction over a number of 9's corresponding to the number of repeating numbers. For example:
0.42984298~ = 4298/9999
0.6~ = 6/9 = 2/3
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But it's .99999999999, not 1. So techinically, It's .9999999999, not 1, because you didn't say it was 1.
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<Kazuki> Wow.
<Kazuki> I feel like stapling Dascoo to the ceiling by his balls.
<Kazuki> I think he just posted in that 0.999~ = 1 topic without reading ANY of it.
That's what people have been arguing for the first half of this thread. :X
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Oh yeah, Kazuki I simply made a typo there.
Yeah I meant what Kazuki said, I can't be bothered to quote it.
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.99999999--> will continually get closer to 1, but never reach it. draw a graph of y=1/x to see a visual example.
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Okay if this was rounding them then just .9 or even .999999999999999999999999999 would be = to 1,but if it was no rounding, then .9 would be closest to one then the more 9's you get the farther you get from a one
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Okay if this was rounding them then just .9 or even .999999999999999999999999999 would be = to 1,but if it was no rounding, then .9 would be closest to one then the more 9's you get the farther you get from a one
Wrong, you get closer with more numbers following in the decimal.
.99 is not closer to 1 then .9
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Thats what i said, .9 is closer then .99
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This is all leading back to what I said already, if at the beginning when they first thought up the concept of a number system they thought about it a lot more than what they obviously didn't, then we wouldn't have friggin problems like these. ANARKY xD
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Deleted spam by The Bone Collector and Dascoo.
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Okay if this was rounding them then just .9 or even .999999999999999999999999999 would be = to 1,but if it was no rounding, then .9 would be closest to one then the more 9's you get the farther you get from a one
Wrong, you get closer with more numbers following in the decimal.
.99 is not closer to 1 then .9
I'm confused. Are you saying that .9 is closer to 1 than .99 or what?
.99 is closer to 1 because it is .09 more than .9 (or .90) and so on and so forth. It's like saying that 99 is closer to 100 than 90.
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But it's Infinity .999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999 999999999999999999999999999999999
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I could count that as spam, but I could just as easily argue that 0.00~1 is infinity as well: 0.00000000000000000000000 ...
And since the zeros continue on infinitely, the 1 at the end never comes into existance, because there is no end. Therefore, the difference between 0.999~ and 1 is 0. See? Call it false logic if you wish, but in doing so you will be dubbing your logic false as well.
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1 divided by 3 -> 0.333333333333..... multiplied by 3 = 0.99999999999999.....
So, 0.9999999......... = 1.
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Dascoo's post reminds me one of the ali g's show where he was interviewing nasa lol
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I like this algebraic proof my university math professor showed us:
a = 0,999...
Multiply by 10: 10a = 9,999...
Substract a: 10a - a = 9
Divide by 9: a = 1
http://en.wikipedia.org/wiki/0.99999
End of discussion!
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Dascoo's post reminds me one of the ali g's show where he was interviewing nasa lol
That's where he gets all his jokes from... >.>
P.S. 0.999~ ≠ 1 because of the 'piece of string' argument QED.
And
I like this algebraic proof my university math professor showed us:
a = 0,999...
Multiply by 10: 10a = 9,999...
Substract a: 10a - a = 9
Divide by 9: a = 1
http://en.wikipedia.org/wiki/0.99999
End of discussion!
No that's just exploiting the algebraic system to prove something that isn't actually true, there are many other things you can 'prove' using it too, but they aren't accurate. THE NUMBER SYSTEM IS FUCKED get a new one earth.
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HOLY CRAP, .999... IS EXACTLY THE SAME AS ONE.
excuse my caps lock but this is a basic elementary fact. I don't see how this can be a debate. It's MATH. Either you're right or wrong. And .999... is EXACTLY 1.
Do you guys think Gauss is wrong? Is Leibnitz lying? They're only like among the top 10 smartest people who ever lived.
Proof 1: fractions.
0.333… = 1⁄3
3 × 0.333… = 3 × 1⁄3
0.999… = 1
Proof 2: algebra.
c = 0.999…
10c = 9.999…
10c − c = 9.999… − 0.999…
9c = 9
c = 1
There's like a million other proofs with more complicated things, but this should be enough.
There's no such thing as .000~1. That's called zero. And no, you can't prove 1=2. They divided by zero. MATH IS MATH, AND IT IS THE LAW. MATH DOESN'T NEED ANYONES OPINION.
YOU CAN'T PROVE SOMETHING THAT ISN'T TRUE, PANZER. MATH IS NOT INACCURATE. THE NUMBER SYSTEM IS PERFECT BY DEFINITION.
RAWR.
and hi.
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Wait I thought I was agreeing with kazuki....
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Okay if this was rounding them then just .9 or even .999999999999999999999999999 would be = to 1,but if it was no rounding, then .9 would be closest to one then the more 9's you get the farther you get from a one
ok the way i see it is that .9 = .900000000000000000 and that is only .1 away from well 1 but .999999999999999999 is only .00000000000000001 away from 1
but since its ,999999999999999999 infinity it would be .000000 infinity zeros and then 1 as the last number since infinity zeros go on forever that dose not work
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.99999999--> will continually get closer to 1, but never reach it. draw a graph of y=1/x to see a visual example.
Plonkoon wins for giving a tangible explination. Applaud.
And swarmer:
0.333… = 1⁄3
is still rounding. Just go with fractions people.
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.99999999--> will continually get closer to 1, but never reach it. draw a graph of y=1/x to see a visual example.
Plonkoon wins for giving a tangible explination. Applaud.
Smite!
0.9999~ is impossible to graph, at least, completely. It's like trying to see where the y = x line ends by making a graph out of it.
And by 0.33333 he meant 0.3333~
AND
Students of mathematics often reject the equality of 0.999… and 1, for reasons ranging from their disparate appearance to deep misgivings over the limit concept and disagreements over the nature of infinitesimals. There are many common contributing factors to the confusion:
* Students are often "mentally committed to the notion that a number can be represented in one and only one way by a decimal." Seeing two manifestly different decimals representing the same number appears to be a paradox, which is amplified by the appearance of the seemingly well-understood number 1.[12]
* Some students interpret "0.999…" (or similar notation) as a large but finite string of 9s, possibly with a variable, unspecified length. If they accept an infinite string of nines, they may still expect a last 9 "at infinity."[13]
* Intuition and ambiguous teaching lead students to think of the limit of a sequence as a kind of infinite process rather than a fixed value, since a sequence need not reach its limit. Where students accept the difference between a sequence of numbers and its limit, they might read "0.999…" as meaning the sequence rather than its limit.[14]
* Some students regard 0.999... as having a fixed value which is less than 1 but by an infinitely small amount.
* Some students believe that the value of a convergent series is an approximation, not the actual value.
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There's no such thing as .000~1. That's called zero. And no, you can't prove 1=2. They divided by zero. MATH IS MATH, AND IT IS THE LAW. MATH DOESN'T NEED ANYONES OPINION.
YOU CAN'T PROVE SOMETHING THAT ISN'T TRUE, PANZER. MATH IS NOT INACCURATE. THE NUMBER SYSTEM IS PERFECT BY DEFINITION.
Yes! SHLAP HANDS!
/me offers a high-five.
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*Accepts high-five
0.9999~ is impossible to graph, at least, completely. It's like trying to see where the y = x line ends by making a graph out of it.
Incorrect. The graph of x = .999~ is the same as the graph of x = 1, since, well, .999~ = 1.
And swarmer:
0.333… = 1⁄3
is still rounding. Just go with fractions people.
NO. .333... is EXACTLY EQUAL to 1/3. It's not rounding.
it would be .000000 infinity zeros and then 1 as the last number since infinity zeros go on forever
If you have infinity zeros you can't add a 1 as the last number. There is no last number. That's the definition of infinity. 1 - .999... = 0.
.99999999--> will continually get closer to 1, but never reach it. draw a graph of y=1/x to see a visual example.
No, you draw a graph yourself and see the fact that it does reach 1. You proved your own point wrong. Rawr.
PEOPLE, MATH IS NOT DEBATABLE. LOOK UP THE SCIENTIFIC ANSWER. .999... IS 100% EXACTLY EQUAL TO 1. It's mathematically proven, and every single credible scientist supports it. This is not a debate. It's a question. And the answer is yes, it is equal to 1.
I think it's okay to not know this fact, because intuitively, it doesn't seem equal. That's okay, we all need to learn. But when you believe with such fervor that it's not equal, when all it takes is a quick search to verify your claims, then you've got a problem.
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Okay if this was rounding them then just .9 or even .999999999999999999999999999 would be = to 1,but if it was no rounding, then .9 would be closest to one then the more 9's you get the farther you get from a one
Wrong, you get closer with more numbers following in the decimal.
.99 is not closer to 1 then .9
I'm confused. Are you saying that .9 is closer to 1 than .99 or what?
.99 is closer to 1 because it is .09 more than .9 (or .90) and so on and so forth. It's like saying that 99 is closer to 100 than 90.
Bah, misunderstandings/mistypings. I thought Wolfman was saying that the more 9s after the decimal, the farther you were from one. Then, I accidentally switched the two numbers when I said "
.99 is not closer to 1 then .9" I meant to say ".9 is not closer to 1 then .99"
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really?well thats what i thought lol cause .9 1.0 and .99 would go to 1.00,hmmm wouldent they be the same!?
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Wolf_man no offence but your 11 and this is a math thread :D haha. Anyways yeah our math system is messed up but who would change it?
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RAWR LIES.
NO IT ****ING IS NOT GARARARAR GREEBL GREEBL.
THERE ARE SO MANY PROBLEMS IN TODAYS WORLD THAT WE CAN'T SOLVE BECAUSE OUR SYSTEM OF NUMBERS IS BULL****.
NO THERE ISN'T. NAME ONE.
IT WORKS IN THE SHORT RUN BUT WHEN WE START HAVING HUGE FORMULAS THAT TAKE DIFFERENT EQUATIONS WORKED OUT THROUGH MANIPULATING NUMBERS LIKE PI AND STICK THEM ALL TOGETHER IT'S SCREEEWED.
GIVE ME A SINGLE EXAMPLE.
PI SHOULD BE A DEFINITIVE VALUE. BUT IT'S NOT BECAUSE OUR NUMBER SYSTEM SAYS *Girlish prancy voice* Ohhhh you can't make pi an exact value because the numbers go on forever *End of girlish prancy voice*
GAHH THAT MAKES NO SENSE. Pi is irrational. Irrational numbers can't be written out completely. The irrationality of pi is the foundation for important proofs and applications that directly affect how you live. Do you like TV? Do you like teh intarwebs? Do you like driving on bridges that don't collapse? These are all possible thanks to pi.
YOU CAN PROVE THINGS THAT AREN'T TRUE (IN THE MINDS OF PEOPLE THAT THINK IT'S TRUE).
NO YOU CANT. NAME A SINGLE EXAMPLE.
EVERYONE WAS SURE THAT THE WORLD WAS FLAT AS MUCH AS THEY WERE SURE 1+1=2 AND THAT WAS THEREFORE SAID TO BE TRUTH, BUT THEN CHRISTOPHER COLUMBUS PROVED THAT IT IS ROUND AND EVERYONE'S *OPINION* WAS CHANGED.
That's a terrible analogy. Math has nothing to do with peoples opinions. Math can't be changed by scientific discoveries. Science is based on math.
LAW IS ALSO SOMETHING THOUGHT UP BY HUMANITY BUT JUST BECAUSE IT'S SOMETHING THAT A LOT OF PEOPLE SAY IS TRUE DOESN'T ACTUALLY MAKE IT TRUE.
Math defines a series of laws, and we're debating within the laws. The metaphysics and philosophy of truth and laws doesn't apply to this argument since we're talking about what happens within these laws.
P.S. Numba system 'aint perfect Grin
RAWRG YES THEY ARE
our math system is messed up but who would change it?
MATH IS NOT MESSED UP, MATH IS PERFECT BY DEFINITION
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EDIT:Dont flame each other
Swarmer. Look at the rules before you tell us what is right or wrong.
YOU CAN PROVE THINGS THAT AREN'T TRUE (IN THE MINDS OF PEOPLE THAT THINK IT'S TRUE).
NO YOU CANT. NAME A SINGLE EXAMPLE.
Look at religion. Look at anything that is deemed as the truth, there always will be inconsistencies.
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Wolf_Man,
Swarmer is using caps to emphasize information that needs to be remembered. He is not whining, but using his knowledge of mathemetics to correct mistakes that he thinks others have made.
And I believe Panzercat's post was a joke post. Correct me if I'm wrong.
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Look at religion. Look at anything that is deemed as the truth, there always will be inconsistencies.
And yet, what are the inconsistencies in math? Can you find any?
I must also ask, are you one of those people who believe there is no absolute truth?
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I'm not talking about rules or laws or truth.
I'm talking about whether .999... equals 1. And it does.
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Without rounding up, 0.99~ is equal to one. You see, all integer numbers can be written in two ways, lets take 1 for example:
1.00000~
0.9999~
Em, remember how to turn numbers with infinite periodic decimals into fractions?
0.444444~ = 4/9
0.323232~ = 32/99
Well, do that with 0.9999~
0.9999999~ = 9/9 = 1
No need to know and understand the idea of limit, just read the explanation above.
This post is correct. My friend linked me this thread and I registered just to enjoy debating with people.
0.9999.... DOES equal 1.00000 because they are simply two different decimal representations of the same number. All numbers that "end" have two different decimal representations - one with trailing zeroes and one with trailing ones.
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Lol
Okay, to swarmer, I'm not saying that maths doesn't work because yes it does. Like you said, otherwise we wouldn't have things like tv and bridges that don't collapse blah blah, but you're missing my point.
Pi is an irrational number yes, but because of humans way of arranging values like pi into what we know as our number system, it makes them undefinable. It goes on forever. If we had a different number system where we could just say BAM x=pi (That fits in with everything else) then we could make calculations perfect.
At the moment we are just going by an inaccurate set of digits that go on forever and therefore we are never going to acheive perfect maths. The same with the .999 = 1 thing. If the number system humans thought up would have been considered more before saying it's perfect then we wouldn't have these problems.
Oh and your probably wanting an example so, take light years and shit. When you go into formula and math that deals with space time and so forth, then that is when maths begins going loopy. Say I needed to calculate some sort of angle in a direction pointed into space (For simplicities sake make it a spaceship that can travel at light speed and needs to go half way across the universe). If we were using math to work out the direction and pi came up in it, the spaceship would be completely fucked and go waaay off course because after that much distance, the inacuracy of pi (And the number system) would make a huge difference.
Whereas if we had, like I said, x=pi then we could just say ok spaceship goes in x direction. AND EVERYTHING WOULD BE CHERRY S0DA F1NE.
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Spam by Wolf_Man, Swarmer, und Panzercatwagon ist kaput. Caps Locking ist kaput.
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Panzercat
Go take a course in real numbers before you start talking about mathematics. I bet you don't even know what 0.999... means.
Date Posted: November 05, 2006, 05:41:33 PM
Oh, and your example regarding pi and the spaceship, that shows inadequate knowledge of what pi is. Go research pi some more.
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Okay anways, this is becoming flamey, and that's not what I want.
No, math is not inaccurate in space.
No, pi is not "innacurate". What you're talking about is if you just rounded off pi as 3.14 something. Then after a long distance you would be way off. That was exactly my point earlier. Pi needs to be infinitely accurate, or things like that happen.
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Pi is an irrational number yes, but because of humans way of arranging values like pi into what we know as our number system, it makes them undefinable. It goes on forever. If we had a different number system where we could just say BAM x=pi (That fits in with everything else) then we could make calculations perfect.
At the moment we are just going by an inaccurate set of digits that go on forever and therefore we are never going to acheive perfect maths. The same with the .999 = 1 thing. If the number system humans thought up would have been considered more before saying it's perfect then we wouldn't have these problems.
Pi IS defineable. It's most certainly a defined number. A number that is NOT defined is something like 1/0. Just because something can't be expressed as a fraction doesn't mean it's not defined. Also, pi is not this way because of "humans way of arranging values like pi into what we know as our number system," it's that way because that's the way the universe works. People didn't INVENT pi. Pi was DISCOVERED to be the ratio of a circle's circumference to its diameter (or its area to the square of its radius).
On topic, the definition of the "..." notation used for 0.999... seems not to be understood. The definition of 0.999... is the limit of the sequence {sum(9/(10^i)) for i from 1 to n} for all natural numbers n. This basically is a precise way of defining the sequence {0.9, 0.99, 0.999, ...}. Every number in that sequence is a real number (a rational number, no less). The limit of this sequence, I'm pretty sure, we can all agree, is 1. Therefore 0.999... = 1.
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Now time to go back and address every math heresy in this thread!
I will first address all "0.999... + 0.000...1 = 1, so 0.999... is not equal to 1" posts. 0.000...1 is NOT A NUMBER because you CANNOT append a 1 onto the "end" of an endless string of zeroes. 0.000...1 is imprecise, misused notation, and even if it WERE correctly used, it would equal zero.
I will next address all "0.999... approaches 1, but doesn't equal 1" posts. 0.999... is a number. It is not a sequence, it is a number. It is defined as the LIMIT of a sequence, but it is ONE NUMBER. One number cannot "approach" anything. The only thing that you can define to approach a value is a sequence. What you're TRYING to say with this statement is that the sequence {0.9, 0.99, 0.999, ...} approaches 1. Since the limit of that sequence is EQUAL to 0.999... by definition, you have proved my point. Thank you.
Now on to kill individual heresies!
PANZERCATWAGON:
The reason all of our maths is screwed is because the stupid guy that invented our number system made it like it is today, which causes problems with things like .999 and infinity.
Incorrect! Our number system is actually VERY precisely defined and there are no visible problems with it as of now (for my credibility, I am taking a course in Real Analysis and a course in Abstract Algebra right now, both of which this topic revolves around).
This is all leading back to what I said already, if at the beginning when they first thought up the concept of a number system they thought about it a lot more than what they obviously didn't, then we wouldn't have friggin problems like these.
The only problem with this concept is people not understanding how things are defined, and misusing math.
No that's just exploiting the algebraic system to prove something that isn't actually true, there are many other things you can 'prove' using it too, but they aren't accurate. THE NUMBER SYSTEM IS ****ED get a new one earth.
It's exploiting the system of algebra, if by "exploiting," you mean "using." Show me the inaccuracy in the logic that makes it "exploiting the algebraic system to prove something that isn't actually true." Show me something false you can prove using valid algebra, and I will be inclined to concede to your point.
Dascoo:
But it's .99999999999, not 1. So techinically, It's .9999999999, not 1, because you didn't say it was 1.
Correct and incorrect. You are correct that .99999999999 does not equal 1. You are incorrect in that you are completely off-topic. We're not talking about .99999999999 here, we're talking about 0.999... a completely different number.
Mistercharles:
0.333… = 1⁄3
is still rounding. Just go with fractions people.
Nope! Not rounding. It WOULD be rounding if you said that 1/3 = 0.333, but it isn't when you say 1/3 = 0.333... Seriously, people need to learn what notation MEANS before they start arguing about it.
Jettlarue:
Look at religion. Look at anything that is deemed as the truth, there always will be inconsistencies.
Oranges aren't orange because apples are red, and therefore not orange. That's essentially what you're arguing. This discussion is about math (by its very nature objective), not about religion (by your as of yet unsubstantiated suppositions subjective).
Bleh, I'd own more people's false statements, but a lot of them were either typos or were already owned by someone else :(
Date Posted: November 05, 2006, 06:19:43 PM
I know people didn't invent pi, I didn't say that. It's the way our number system sets it out like that, which is the cause of humans making the number system like that in the first place.
EDIT: Ugh .. ok so like instead of using 1 and 2 and 3 etc. we could have something completely different, not even necessarily in consecutive order. Hmm ... it's a hard concept to grasp because it's almost unimaginable, seeing as it's nothing we've never seen or used. But it would be really weird anywho. Ugh, I can't even be bothered to think about this now... Tongue
Okay, I see where you're going with this now. Sure, we could define pi to be something that doesn't repeat. However, if we do this, then every time you want to say something like "I have one apple," that "one" would be a repeating decimal. Every time you used the number one in calculations, it would be a repeating decimal. All integers as we use them would have to be irrational (I'm fairly certain) in order for pi to be a rational number, by a different definition of numbers.
I'll have more on this after I get done studying how we define the real number system based on the rational number system this week in Abstract Algebra.
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Why don't we use binary? Be alot simpler imo.
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Wow, that's annoying and weird that when you edited your post, it bumped it below mine, in which I REPLIED to your post. Strange forums :P
But on to the point, if you're saying that we could use some kind of token number to represent pi, then I have nothing to say but that we already have.
In response to this:
There could even be more intelligent beings out there that have 'perfect maths'. Hate saying that cause I know you're going to moan, but they could come here and prove our ideas of maths and science to be bull****.
You're basically stating (as far as I can tell) that every number should have a finite decimal representation, or in other words, every real number should be rational. You're claiming that there IS a way to do this. My first response is: Prove it. The burden of proof rests on you, my friend, because the real number system as it is now seems perfectly well defined to me and all the brilliant mathematicians in the world. My second response is one you won't understand. You are claiming that there does exist a bijection between the rational numbers and the real numbers, a statement which can be and has been proven to be false, by extension of Cantor's proof that there is no bijection from the natural numbers to the interval (0,1), a proof I can duplicate if need be :P
Date Posted: November 05, 2006, 06:34:55 PM
Why don't we use binary? Be alot simpler imo.
We could. All real numbers have a binary representation :P
Doesn't change the fact that irrational numbers would exist though. Also doesn't change the fact that, in binary, 0.11111... = 1.
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No I'm not talking about rounding it off, I'm talking about keeping pi accurate without it being infinite. As in if you add one to one you can get to exactly two, you should be able to say just x for pi and have it still be accurate. We can't do that with our number system and that is what I am saying is wrong with our maths.
I don't know of a way of doing it, don't think I know :P
Oh and
Pi IS defineable. It's most certainly a defined number. A number that is NOT defined is something like 1/0. Just because something can't be expressed as a fraction doesn't mean it's not defined. Also, pi is not this way because of "humans way of arranging values like pi into what we know as our number system," it's that way because that's the way the universe works. People didn't INVENT pi. Pi was DISCOVERED to be the ratio of a circle's circumference to its diameter (or its area to the square of its radius).
On topic, the definition of the "..." notation used for 0.999... seems not to be understood. The definition of 0.999... is the limit of the sequence {sum(9/(10^i)) for i from 1 to n} for all natural numbers n. This basically is a precise way of defining the sequence {0.9, 0.99, 0.999, ...}. Every number in that sequence is a real number (a rational number, no less). The limit of this sequence, I'm pretty sure, we can all agree, is 1. Therefore 0.999... = 1.
I know people didn't invent pi, I didn't say that. It's the way our number system sets it out like that, which is the cause of humans making the number system like that in the first place.
EDIT: Ugh .. ok so like instead of using 1 and 2 and 3 etc. we could have something completely different, not even necessarily in consecutive order. Hmm ... it's a hard concept to grasp because it's almost unimaginable, seeing as it's nothing we've never seen or used. But it would be really weird anywho. Ugh, I can't even be bothered to think about this now...
Hmm, a way of thinking about it is sort of like money, in the industialised world we use coins and notes and cheques as a forum of currency. But in certain situations like in tribes and such currency can be things like food, women or even luck etc. These obviously aren't accurate and don't go start thinking I'm saying we should all stop using money and throw women around instead.
Cause if we went to a different planet with, say aliens that are intelligent enough, they would have a completely different ... everything to us. Some things would be the same such as prescence of elements and such, although there may be additional elements that we haven't discovered yet and things like discovering radio and fire and stuff. I'm not very imaginitive though so I can't give an example of what their life might be like :P But it would could be completely different.
There could even be more intelligent beings out there that have 'perfect maths'. Hate saying that cause I know you're going to moan, but they could come here and prove our ideas of maths and science to be bull****.
Man, I've still got to get up early in the morning tommorow ;_____;
:P
And if you look, I actually stated that 0.999~ should equal 1 ... so yeah :P
I know people didn't invent pi, I didn't say that. It's the way our number system sets it out like that, which is the cause of humans making the number system like that in the first place.
EDIT: Ugh .. ok so like instead of using 1 and 2 and 3 etc. we could have something completely different, not even necessarily in consecutive order. Hmm ... it's a hard concept to grasp because it's almost unimaginable, seeing as it's nothing we've never seen or used. But it would be really weird anywho. Ugh, I can't even be bothered to think about this now... Tongue
Okay, I see where you're going with this now. Sure, we could define pi to be something that doesn't repeat. However, if we do this, then every time you want to say something like "I have one apple," that "one" would be a repeating decimal. Every time you used the number one in calculations, it would be a repeating decimal. All integers as we use them would have to be irrational (I'm fairly certain) in order for pi to be a rational number, by a different definition of numbers.
I'll have more on this after I get done studying how we define the real number system based on the rational number system this week in Abstract Algebra.
Okay then :P
By the way, you are quite fun to argue with ;D
Oh yeah and...
It's exploiting the system of algebra, if by "exploiting," you mean "using." Show me the inaccuracy in the logic that makes it "exploiting the algebraic system to prove something that isn't actually true." Show me something false you can prove using valid algebra, and I will be inclined to concede to your point.
I'm sure you must have seen at least one of these, judging by those credentials :P.
They are things like 0 = 1, 1 = 2 and some others that I can't remember, say 4 = 12 (That one I don't know how to do, because I just made it up, but it's just an example). These things are obviously wrong because 1 obviously cannot equal 2, but using formula they can rearange them in various ways so they end up like that. That's all I meant, wasn't really anything to important though.
EDIT:
Wow, that's annoying and weird that when you edited your post, it bumped it below mine, in which I REPLIED to your post. Strange forums
'Tis not the forums :P I deleted my old message and reposted it to save clogging up the forums with lots of small posts when it can just be one big post, like this.
But on to the point, if you're saying that we could use some kind of token number to represent pi, then I have nothing to say but that we already have.
Yes we do but it's still calculated using this number system.
You're basically stating (as far as I can tell) that every number should have a finite decimal representation, or in other words, every real number should be rational. You're claiming that there IS a way to do this. My first response is: Prove it. The burden of proof rests on you, my friend, because the real number system as it is now seems perfectly well defined to me and all the brilliant mathematicians in the world.
I can't prove it, and I don't intend on trying to, it's just too insanely difficult. It can be accomplished, but not by me, probably by the next Einstein. I'd rather just point it out and critisise then take action. Wrong, I know :P
My second response is one you won't understand. You are claiming that there does exist a bijection between the rational numbers and the real numbers, a statement which can be and has been proven to be false, by extension of Cantor's proof that there is no bijection from the natural numbers to the interval (0,1), a proof I can duplicate if need be
Naw, I jest need sleep right now :P
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They are things like 0 = 1, 1 = 2 and some others that I can't remember, say 4 = 12 (That one I don't know how to do, because I just made it up, but it's just an example).
Those involve dividing by zero, which is not valid algebra. All the steps in the x = .999..., so 10x = 9.999..., so 9x = 9, so x = 1 proof are VALID.
I can't prove it, and I don't intend on trying to, it's just too insanely difficult. It can be accomplished, but not by me, probably by the next Einstein.
The sky is pink with purple polkadots. I can't prove it, but it's true. Someone will prove it later, because it CAN be done.
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I can't prove it, and I don't intend on trying to, it's just too insanely difficult. It can be accomplished, but not by me, probably by the next Einstein.
The sky is pink with purple polkadots. I can't prove it, but it's true. Someone will prove it later, because it CAN be done.
Lol, yeah, it sounds a bit farfetched. But think of it like the spaces in the periodic table of elements, there are spaces in there for elements by the periodicity shown, but we haven't discovered them yet and so we can't prove it. But later on we will have dicovered these elements and therefore they are proved to exist.
I SERIOUSLY HAVE TO GO TO BED NOW THOUGH ... ;___;
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.99999999--> will continually get closer to 1, but never reach it. draw a graph of y=1/x to see a visual example.
Yeah I agree with that, but its kinda confusing.
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http://en.wikipedia.org/wiki/Proof_that_0.999..._%3D_1
Enough said.
This is a well known proof that 0.999... == 1.
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Anyone that argues that .9999... is not equal has no knowledge of modern mathematics. Ask any professer, math teacher, etc, and they will say you are wrong. It' a matter of simple fractions people.
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Math is something humans made up. Humans aren't perfect, thus making math not perfect. Math is very weird. Even though I don't like to beleive that .999 =1 I do. if you look at it with math, .999=1. If you look at it with logic, .999 does not equal 1. To me .999 =1 or not by depending on WHO does the math.
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It's fun to watch nerds argue :>
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^And it's fun to be called a nerd. I <3 ASTROPHYSICS. Not physics, normal physics suck.
But still, if if you did graph .999 technically it should never equal 1. Oh and just to be a total pain, Wikipedia is not being called a credible source now chrisgbk.
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Math is something humans made up. Humans aren't perfect, thus making math not perfect. Math is very weird. Even though I don't like to beleive that .999 =1 I do. if you look at it with math, .999=1. If you look at it with logic, .999 does not equal 1. To me .999 =1 or not by depending on WHO does the math.
This guy wins the thread. The first part was pretty dumb, but this part
if you look at it with math, .999=1. If you look at it with logic, .999 does not equal 1.
solves the thread.
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^Thank you nubface. Problem solved gais.
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Blargh. Stop saying .999 doesn't equal 1. This thread isn't even about the number 0.999, it's about the repeating decimal 0.999... - the two are COMPLETELY different numbers. And as I've said again and again, it's equal to one very clearly from the very definition of the ... notation.
Math is something humans made up.
And math is a beautiful and elegant representation and analysis useful to and applicable to many things in nature :P
You'd be surprised how much certain mathematical concepts that SEEM abstract (calculus, physical constants, even prime numbers) apply to naturally occuring phenomena.
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Math is something humans made up. Humans aren't perfect, thus making math not perfect. Math is very weird. Even though I don't like to beleive that .999 =1 I do. if you look at it with math, .999=1. If you look at it with logic, .999 does not equal 1. To me .999 =1 or not by depending on WHO does the math.
This guy wins the thread. Â The first part was pretty dumb, but this part
Actually, if humans also made up the concept of perfection, and if human aren't perfect then perfection isn't perfect , and you've found yourself a paradox. And is now impossible to say whether or not anything is perfect.
BUT, if humans are perfect, then perfection is perfect and math is perfect, but this would also mean that, being perfect, anything a human states as true is true and states as untrue is untrue, and people contradict eachother all the time, so you have another paradox.
But, the concept behind math is not to be perfect, but to be true. It is what makes 1=1, 2=2 and so on. So unless something stated with math is proven wrong then it is true.
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Math is something humans made up. Humans aren't perfect, thus making math not perfect. Math is very weird. Even though I don't like to beleive that .999 =1 I do. if you look at it with math, .999=1. If you look at it with logic, .999 does not equal 1. To me .999 =1 or not by depending on WHO does the math.
Math wasn't invented, it's like saying the gravity was invented. Math is assigning characters to things and discovering the rules that govern them. Just like any cience!
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Math is assigning characters to things and discovering the rules that govern them.
But, in the end, that doesn't make it different from something being "invented" to something being discovered.
Actually, if humans also made up the concept of perfection, and if human aren't perfect then perfection isn't perfect , and you've found yourself a paradox. And is now impossible to say whether or not anything is perfect.
It wouldn't be a paradox, because you are assuming too much.
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.999 recurring/repeating/whatever is .999 recurring/repeating/whatever. 1 is 1. .999 recurring/repeating/whatever LOGICALLY! is not 1.
EDIT: Logic rocks.
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Logic failed.
This is what you are saying:
Statement A: .999... = .999...
Statement B: 1 = 1
Conclusion: Therefore, .999... is not 1
Now that's like saying this:
Statement A: All ducks are ducks.
Statement B: All birds are birds.
Conclusion: Therefore, ducks are not birds.
There's no rule that says every number can only be written one way.
The number 1 can be written an infinte number of ways, such as:
1/1, or 4346/4346, or pi/pi, or x/x, or x^0, or 0!, or even .999....
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so bascally its a glitch in math and those sientists that decided pluto is not a planet any more have to decide it if .9999 = 1 or not?
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No, it's not a glitch in math. Math doesn't have glitches. 0.999... is exactly 1. The people who disagree are wrong. Plain and simple. Read the proofs. Ask your professor. If he disagrees with me then stab him with a pen and tell those in charge to fire him.
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Logic failed.
This is what you are saying:
Statement A: .999... = .999...
Statement B: 1 = 1
Conclusion: Therefore, .999... is not 1
Now that's like saying this:
Statement A: All ducks are ducks.
Statement B: All birds are birds.
Conclusion: Therefore, ducks are not birds.
There's no rule that says every number can only be written one way.
The number 1 can be written an infinte number of ways, such as:
1/1, or 4346/4346, or pi/pi, or x/x, or x^0, or 0!, or even .999....
We're not comparing apples to oranges here. It's more like different kinds of apples.
Red Apples are Red Apples
Green Apples are Green Apples
Therefore, Red Apples are not Green Apples
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There's no rule that says every number can only be written one way.
The number 1 can be written an infinte number of ways, such as:
1/1, or 4346/4346, or pi/pi, or x/x, or x^0, or 0!, or even .999....
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Logic failed.
This is what you are saying:
Statement A: .999... = .999...
Statement B: 1 = 1
Conclusion: Therefore, .999... is not 1
Now that's like saying this:
Statement A: All ducks are ducks.
Statement B: All birds are birds.
Conclusion: Therefore, ducks are not birds.
There's no rule that says every number can only be written one way.
The number 1 can be written an infinte number of ways, such as:
1/1, or 4346/4346, or pi/pi, or x/x, or x^0, or 0!, or even .999....
We're not comparing apples to oranges here. It's more like different kinds of apples.
Red Apples are Red Apples
Green Apples are Green Apples
Therefore, Red Apples are not Green Apples
All numbers are greater than zero.
Proposed counterexample: You're wrong because -1 < 0.
You: No, no, 1 > 0, so I'm right.
Date Posted: November 06, 2006, 12:23:37 AM
For a more relevant example of Swarmer's point!
The multiplicative identity is the multiplicative identity.
One is one.
Therefore the multiplicative identity is not one.
Edit: Grammar.
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We're not comparing apples to oranges here. It's more like different kinds of apples.
Red Apples are Red Apples
Green Apples are Green Apples
Therefore, Red Apples are not Green Apples
You do realize you're only aiding in proving Swarmers point, right?
It may not look like 0.9999~ is 1, but it is. The proofs are out there, do the math for yourself, end of story. Simple logical proofs like that really have no place in the arguement.
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.999... is .999.... 1 is 1. .999... LOGICALLY! is not 1.
EDIT: Logic rocks.
Your logic fails, actually. If a = c and b = d, it's still possible to have c = d. However, if a = c and a =! d, you could say c =! d.
For instance, 2 x 2 = 4 and 5 - 1 = 4. A = B = C = D.
You might not understand this because you don't have a good grasp of either infinity or limits. The article chrisbk linked to (http://en.wikipedia.org/wiki/Proof_that_0.999..._%3D_1) has a very nice set of proofs that you'd understand, have a look at it.
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I realize my logic fails, I'll check that link, and disregard any posts I made that state that .999~ != 1
EDIT: Hmmmmm, does 1.000~1 = 1 ?
>_>
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There's no such thing as 1.000~1, it's simply 1.0000~ (1) because the 1 never appears.
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EDIT: Hmmmmm, does 1.000~1 = 1 ?
>_>
Well, you can't really have a .000~1. If the zeros go on infinitely there's no "end" to put the 1 on. Think of it as 1/(10^x), with x getting bigger and bigger towards infinity.
x = 1: 1/10 = .1
x = 2: 1/100 = .01
x = 3: 1/1000 = .001
etc.
And for .000~1 you need x to be infinity. However, infinity is not a number. You have to take the limit as x goes to infinity. The limit of 1/(10^x) as x goes to infinity equals zero. So .000~1 equals zero.
So yes, 1.000~1 equals 1, but .000~1 isn't really conventional.
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Swarmer's on the right track, but it's much easier to write it as 1 + 1/(10^x). As x → ∞, 1 + 1/(10^x) → 1.
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Meh... it's close enough :P
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<3 Math
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... so should i take how many of you said its 1.. and add them up and how many of you said it isnt an who ever has the most wins?
or is there real proof of something because all those numbers are confusing the heck out of me.
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... so should i take how many of you said its 1.. and add them up and how many of you said it isnt an who ever has the most wins?
or is there real proof of something because all those numbers are confusing the heck out of me.
Gotta love math. ;)