My Junior Year math teacher showed us the proof for this, it's sweet. Damn, I loved his class.

The answer is a complete undoubtable Yes.

.999... = 14.7 because I said so.

I win.

Yes, for all practical purposes it is lim(n-->INF) SUM[0.9( 0.1 ^ n )] is 1. Pommy's proof basically hammers it straight into the ground.

Well the basis of the problem is that it's a plane that's sitting, gear down, on a conveyor belt that's programmed to move backwards at the same speed that the plane moves forwards.

So really, the belt is immaterial, the only thing different is that you'll get to takeoff speed and the wheels will be spinning twice as fast as they normally would. It'll introduce a small amount of friction, but nowhere near enough to actually stop the plane from taking off.

A lot of people assume that the plane would remain stationary, which would be true for a car that gets its forward motion from the wheels. But since a plane flies by thrusting through the air, the conveyor belt can't stop it. If there was a big fan instead of a big conveyor belt, that blew air forward at the same velocity as the propellor was blowing it backwards, then it wouldn't be able to take off.

Maybe the mythbusters should do this one. Oh well. At very least you can get around the problem by assuming a VTOL airplane like the Osprey or Harrier. :p

The plane couldn't take off because it's not moving, and no air is being pushed under its wings.

And I concede the .99 thing... I found this interesting, though:

[QUOTE=Numenor King]given: a = b

a^2 = ab

a^2 + a^2 = ab + a^2

2(a^2) = ab + a^2

2(a^2) - 2ab = ab + a^2 - 2ab

2(a^2) - 2ab = a^2 - ab

2(a^2 - ab) = 1(a^2 - ab)

[edited here down]

c = (a^2 - ab)

2c = 1c

2c - 1c = 1c - 1c

1c = 0

1(a^2 - ab) = 0

a^2 - a^2 = ab - ab = 0

0 = 0

END![/QUOTE]

I hate it when math does that to me...



And for the hell of it, my own (BS) proof: you CAN take the square root of -1!!! :p

Sqrt(-1) = (-1)^(1/2)

(-1)^(1/2) = (-1)^(2/4)

(-1) ^ (2/4) = ((-1)^2)^(1/4)

((-1)^2)^(1/4) = (1)^(1/4)

(1)^(1/4) = 1

Therefore:

Sqrt(-1) = 1

.999 = a number!!11111LOL

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[QUOTE=Vincent Valentine]The plane couldn't take off because it's not moving, and no air is being pushed under its wings.
[/QUOTE]

Why isn't it moving? What's stopping it?

The plane gains its acceleration via it's jet engines/propellers which are pushing against the air not the ground. The movement of the aircraft is mostly independent of the ground.

Ah, nevermind, I get it now.

Okay, cool.

This is a good explanation: http://txfx.net/2005/12/08/airplane-on-a-conveyor-belt/

about this plane thing: wtf? That sucker's not going anywhere. Jon`C is right.

Ugh, maths. Why waste your time on something as unimportant as if 0.99999999999999999999999999999etc = 1?

Because that's what mathematicians and scientists do.

I don't think you understood what I said.

In real life the plane would take off. For the sake of argument, if the treadmill was (theoretically) able to slow the plane, it wouldn't.

According to the problem statement, there is no forward motion relative to the conveyor belt. (the treadmill is going 100mph and so is the plane) How could it possible move? It isn't moving forward because of the conveyor and it isn't moving up because there is no area of low pressure over the wings.

The jet engines push against the air. Landing gear is designed to reduce friction against the ground: the faster the treadmill goes backwards, the faster the wheels turn.

So the conditions in the problem are impossible then and this is all pointless to argue about?

Pommy's proof is the answer. .9999 != 1 .99999999 != 1 .999999999999999999999999999999999999999999 != 1. However .9999.... = 1 By the use of an infinite series.

nah, they're totally different.

just look at them, theres no way they're the same, one of them is loads of characters, whilst the other one is just a line.

so visually, no.

mathematically... i dont care :p

Pretty much. In an ideal situation (where there is no loss to friction between the wheels and wheel base, or inside the treadmill; and where there is absolute friction between the wheel surface and the treadmill), the jet will just keep accelerating trying to accelerate forever without any change in its position.

However, in real life, friction will prevail and the jet will take off.

Edit: Actually, on second thought, that wouldn't affect anything either. If there's no friction between the wheel and the wheel base there's no way for the momentum of the treadmill to be passed on to the aircraft chassis.
No, that airplane is taking off no matter what.

I keep imagining a conveyor belt placed on the edge of a lake (or something) just to make sure there's no cheating involved.

anyone got a radio controlled airplane and a treadmill

You all (with the exception of those who don't :p) forget that an airplane doesn't move because it's wheels turn, but that the wheels turn when the airplane moves on the ground. The propeller/jet/whatever moves the plane forward. And that is independent of what goes on on the ground. How else could an airplane move through the air? A car hanging in the air can't drive forward, because the wheels are supposed to move the ground behind the car, thus pulling the car forward. An airplane moves the air behind it, thus pulling itself forward.
Aeroplanes don't drive, they roll.

[QUOTE=IRG SithLord]Because that's what mathematicians and scientists do.[/QUOTE]

Please please enlighten me. Since when did any of you become mathematicians or scientists?

Anyone can be one. It's just a matter of quality.

There's a lot of them here.

I have studied my fair share of calculus, discrete maths, linear algebra (continuing), statistics and probability, and physics. While I'm not a renouned mathematician, I'm not an idiot to math.

given an ideal situation (no friction, negligable air resistence) the plane would never take off. the jet engines won't do anything at all unless there is air getting under the wings to provide the upward thrust of the plane.

and yeah, .999 != 1 unless you are talking about infinite series.

Gar. That airplane question is annoying. It's not a question of how an airplane lifts, as it seems, but a question of how an airplane moves itself forward. Stupid.

0.999... = 42 :p had to be done.

In all real situations, it would be taken to = 1 especially so in physics, although it has to be 0.999... and not 0.99999999999999 because that is totally different and depending on what you are doing measurable.

This is of course neglecting the proof thats been shown to be valid and which should put it beyond doubt.

[edit]ooppsss [/edit]

[QUOTE=James Bond]it has to be 0.999! and not 0.99999999999999 because that is totally different and depending on what you are doing measurable.[/QUOTE]! is the symbol for a factorial, not a repeating decimal.

Uh... don't factorials kinda have to be integers to be meaningful?

me, not knowing anything about calc, said no. thanks for enlightening me, and now I know where to go for math homework!

It's close enought to 1. Any Engineer would consider anything over 0.999 to be 1 exactly. Who cares what the concept is when in praticality it's not used.



That's not the assumption of the problem. That's just what the problem would lead you to believe. It's one of those problems that check to see if you're really paying attention. Kinda like the question that says "A play carrying passengers that are citizens of both the US and Mexico crashes exactly on the US/Mexico boarder. Where do you bury the survivors?"

In the problem of the airplane, the wheels end up just doing double work.

Actually they taxi. :p

Yes.

Now, if it was .999...!, you'd have an integer. :em321:

0.999...! = 1. :p

friend14: welcome to page 2. I hope you enjoyed not reading it.

I thought 1! = 0?

The airplane would not take off. There would be no lift! It isn't actually moving, and therefore there is no air moving over and under its wings, and therefore it would not be able to take off! It would just continue to sit there in the same place with the conveyor belt running under its wheels.