Wacky infinites headache

People are not supposed to think about silly stuff like that. We're supposed to eat ice cream and collect rare pokemons.

In Hell, Pureghetto makes the threads.

To answer peeg's question, Galileo's paradox:

First, observe that every number it is either a square or not a square. 4 is a square, 7 is not.
- Since every square is also a number, we must conclude that there exist more numbers than squares.
- But for every square there exists exactly one root which is a number, and for every number there exists exactly one square, so there can't possibly be more numbers than squares or vice versa.

By the first point, since there exist numbers that are not squares we would expect the conclusion that there is no one to one correspondence between { x in {squares} } and { x in {numbers} }, however, this does not follow, since there does not exist a number without a square, and there does not exist a square without a number (or root).
This implies that under the function f: R->R; x->x^2, every element of the domain (x) has a corresponding element in the co-domain (x^2). There are as many Xs as there are X^2s.

So despite mathematical evidence to the contrary, we are forced to conclude that there is a one to one correspondence between any infinite subset of infinity under the given relation. Put simply, even though a line with infinity points is twice as long as another line with infinity points, there do not exist more points on one than the other.

Schrödinger's cat

Quantum Mechanics and Cats, two of the universe's biggest mysteries :D

http://upload.wikimedia.org/wikipedi...dinger_cat.png

Quote:

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Originally Posted by o_O

To answer peeg's question, Galileo's paradox:

First, observe that every number it is either a square or not a square. 4 is a square, 7 is not.
- Since every square is also a number, we must conclude that there exist more numbers than squares.
- But for every square there exists exactly one root which is a number, and for every number there exists exactly one square, so there can't possibly be more numbers than squares or vice versa.

By the first point, since there exist numbers that are not squares we would expect the conclusion that there is no one to one correspondence between { x in {squares} } and { x in {numbers} }, however, this does not follow, since there does not exist a number without a square, and there does not exist a square without a number (or root).
This implies that under the function f: R->R; x->x^2, every element of the domain (x) has a corresponding element in the co-domain (x^2). There are as many Xs as there are X^2s.

So despite mathematical evidence to the contrary, we are forced to conclude that there is a one to one correspondence between any infinite subset of infinity under the given relation. Put simply, even though a line with infinity points is twice as long as another line with infinity points, there do not exist more points on one than the other.

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Win. I came back to this thread hoping to explain it, and o_O explains it.

yay

So is ∞/∞ 1 or ∞?
and whats ∞-∞?
the only use i have for infinity is right way up smilies

∞
/
_

Quote:

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Originally Posted by blackmage_nuke

So is ∞/∞ 1 or ∞?
and whats ∞-∞?
the only use i have for infinity is right way up smilies

∞
/
_

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Infinity is not a number so nothing you said made sense :)

Quote:

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Originally Posted by Pureghetto

Quote:

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Originally Posted by blackmage_nuke

So is ∞/∞ 1 or ∞?
and whats ∞-∞?
the only use i have for infinity is right way up smilies

∞
/
_

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Infinity is not a number so nothing you said made sense :)

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Anything can make sense if you look deep enough and believe it :)

Quote:

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Originally Posted by Pureghetto

Win. I came back to this thread hoping to explain it, and o_O explains it.

yay

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Sorry. :p

Why then, is a mosquito capable of halting a train when the two collide while travelling in opposing directions?

Quote:

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Originally Posted by o_O

Quote:

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Originally Posted by Pureghetto

Win. I came back to this thread hoping to explain it, and o_O explains it.

yay

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Sorry. :p

Why then, is a mosquito capable of halting a train when the two collide while travelling in opposing directions?

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Trains need to travel in opposite directions to collide, unless one train is travelling faster than another, on the same track. So I have that figured out.

I can't figure out how a mosquito has to do with it :(

Quote:

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Originally Posted by blackmage_nuke

So is ∞/∞ 1 or ∞?
and whats ∞-∞?
the only use i have for infinity is right way up smilies

∞
/
_

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Both questions: the answer is ∞

∞*∞= ∞
Divide both sides by ∞, and you get ∞ = ∞ / ∞
∞+∞= ∞
Subtract ∞ from both sides, and you get ∞ = ∞ - ∞

2 + 2 = 4!!!

Quote:

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Originally Posted by Firo Volondé

Quote:

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Originally Posted by blackmage_nuke

So is ∞/∞ 1 or ∞?
and whats ∞-∞?
the only use i have for infinity is right way up smilies

∞
/
_

---

Both questions: the answer is ∞

∞*∞= ∞
Divide both sides by ∞, and you get ∞ = ∞ / ∞
∞+∞= ∞
Subtract ∞ from both sides, and you get ∞ = ∞ - ∞

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Huh? ∞ isn't a number

Quote:

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Originally Posted by Pureghetto

Quote:

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Originally Posted by o_O

Why then, is a mosquito capable of halting a train when the two collide while travelling in opposing directions?

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Trains need to travel in opposite directions to collide, unless one train is travelling faster than another, on the same track. So I have that figured out.

I can't figure out how a mosquito has to do with it :(

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Let the mosquito be travelling north, and the train south on the same line. Therefore, their directions are in direct opposition to one another.
When they collide, obviously the outcome is that the mosquito and the train are both travelling south at the initial velocity of the train. Looking at the velocity vector of the mosquito, if north is 0 degrees, the initial velocity = d_m m/s^-1 at 0 degrees. The final velocity is d_t at 180 degrees. Since their initial directions are exactly opposite, they remain on the same line at all times. Since it's a physical impossibility for the mosquito to instantly change velocity we have to assume that there is some form of acceleration involved, and since the directions are opposite the acceleration occurs on the same line. If this is the case, the mosquito must first decelerate to zero m/s^-1 and then accelerate to the speed of the train in the reverse direction.
If the mosquito is touching the train at a velocity of zero m/s^-1 then the train must also be travelling at zero m/s^-1 and therefore be stationary.

That was told to me by my 6th form physics teacher, but just looking at that now, it seems like that reasoning assumes inelastic matter so I don't know how the elasticity of the mosquito affects the outcome. I'm a maths major, not a physics major. :p

P.S. Neither ∞/∞ or ∞ - ∞ equal ∞; both operations are indeterminate.

I can tell Pureghetto will enjoy this:

tldr