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My friends and I got into some heated arguments about these questions, so I decided to share them with SF to see what you guys think:Imagine an airplane standing on a gigantic treadmill. The plane is taking off, but the treadmill is moving in the opposite direction at the exact same speed. Would it still be able to lift off?Is 0.999... equal to 1?What would you consider to be a "big midget"? Where is the line between a big midget and a small person?
Quote from: Kszchroink on October 05, 2007, 07:56:23 amMy friends and I got into some heated arguments about these questions, so I decided to share them with SF to see what you guys think:Is 0.999... equal to 1?Yes and no. It's like asking what 00 is. Zero to any power is zero, but any number to the zeroth power is one.The simplest proof for your question is as follows:1/3 = .333...3 * 1/3 = 3 * .333...1 = .999...The simplest refutation for that claim is that 1 - .999... = .0000...01.
My friends and I got into some heated arguments about these questions, so I decided to share them with SF to see what you guys think:Is 0.999... equal to 1?
Do you have a point to make?
1) Depends on how fast the plane is moving relative to the air around it; if you tethered the plane to the ground and the wind was blowing hard enough, you could generate lift. Think of a kite. It's very unlikely, unless the plane was anchored to the treadmill and the treadmill anchored to the ground, that the plane would be able to stay on the treadmill, but if it was possible, then there would be no lift. Ever seen an automotive testing facility, where they have cars on rollers so the car can accelerate but not move? There is no wind generated in that circumstance, same as there would be only whatever breeze happened to be blowing which would be the same for another observer, and thus, no lift. So long as the plane is able to stay on the treadmill, and the treadmill also doesn't move.
My friends and I got into some heated arguments about these questions, so I decided to share them with SF to see what you guys think:Imagine an airplane standing on a gigantic treadmill. The plane is taking off, but the treadmill is moving in the opposite direction at the exact same speed. Would it still be able to lift off?