.99999999 infinity = 1?

[jettlarue]

Wolf_man no offence but your 11 and this is a math thread haha. Anyways yeah our math system is messed up but who would change it?

[Swarmer]

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

[jettlarue]

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.

[Eagles_Arrows]

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.

[Acetylcholine]

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?

[Swarmer]

I'm not talking about rules or laws or truth.

I'm talking about whether .999... equals 1.  And it does. 

[Omri143]

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?

Code: [Select]

0.444444~ = 4/9
0.323232~ = 32/99

Well, do that with 0.9999~

Code: [Select]

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.

[PANZERCATWAGON]

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.

[VijchtiDoodah]

Spam by Wolf_Man, Swarmer, und Panzercatwagon ist kaput.  Caps Locking ist kaput.

[Acetylcholine]

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 PMOh, and your example regarding pi and the spaceship, that shows inadequate knowledge of what pi is.   Go research pi some more.

[Swarmer]

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.
 

[Omri143]

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.

[Omri143]

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.

[jettlarue]

Why don't we use binary? Be alot simpler imo.

[Omri143]

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

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

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

Doesn't change the fact that irrational numbers would exist though. Also doesn't change the fact that, in binary, 0.11111... = 1.

[PANZERCATWAGON]

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

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 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 ;_____;


And if you look, I actually stated that 0.999~ should equal 1 ... so yeah

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

By the way, you are quite fun to argue with

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 .

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 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

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

[Omri143]

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.

[PANZERCATWAGON]

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 ... ;___;

[The Red Guy]

.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.

[chrisgbk]

http://en.wikipedia.org/wiki/Proof_that_0.999..._%3D_1

Enough said.

This is a well known proof that 0.999... == 1.