Wacky infinites headache

..well not really if you understand it, but some people might get their brains to explode. I'm trying to do this here.

There's two ways to do this: the numbers way and the square way

Numbers way:

I will first prove that there are infinite real numbers between any two integers.

for any real number x between 0 and 1 (say, 0.5 or 0.25) you have another number x/2 or x/y where y is a real number. Doesn't matter. You can do this for any of them. Since you can progressively divide x / y^whatever, there's always another number.

I'll assume you understand. Moving on.

We now have established infinite numbers between 0 and 1. What about 1 and 2? 1 and 2 also has infinite numbers between them. The set is the same as the first set, with each number increased by 1.

But wait, we now have two sets of infinite numbers.

I now ask you. How many numbers between 0 and 2? The answer: infinity.

So we have infinite numbers between 0 and 1 and infinite numbers between 1 and 2 and infinite numbers between 0 and 2.

confusing the average person time: OMG THERE'S THE SAME AMOUNT NUMBERS BETWEEN 0 AND 2 AND 0 AND 1 AND 1 AND 2, EVEN THOUGH I CAN COUNT TWICE THE AMOUNT OF NUMBERS BETWEEN 0 AND 2 AND 0 AND 1 BY TRACING EACH NUMBER TO ITS CORRESPONDING POINT BETWEEN 1 AND 2 LOLOLOLOLOLOLOL

SQUARE METHOD

I have to do this fast cuz I posted too quick.

- infinite points in a line, right? (see number portion for proof)
- infinite points in 2nd line, right?
- how many points in a square?
- infinity? more than infinity? wtf?

solution to problem = where?



Actually don't answer that just yet. Maybe some people will post and go 'wtf my brain hurts'.

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Originally Posted by Pureghetto

'wtf my brain hurts'.

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Remember, ∞ + ∞ = ∞ and ∞ * ∞ = ∞. There's no such thing as 2∞ or something like it. Infinity is not a variable like x. Thus, the numbers between 0 and 1 are ∞ and 1 and 2 are ∞, or ∞ + ∞ = ∞.

I hope that makes sense.

Yeah it does, it just seemed as though he couldn't continue without someone saying "my brain hurts", so I said it.

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Originally Posted by Flying Mullet

Remember, ∞ + ∞ = ∞ and ∞ * ∞ = ∞. There's no such thing as 2∞ or something like it. Infinity is not a variable like x. Thus, the numbers between 0 and 1 are ∞ and 1 and 2 are ∞, or ∞ + ∞ = ∞.

I hope that makes sense.

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Intuitively this works, and anybody with an understanding of the term infinity knows this.

I'm messing with your brain by saying that there IS a 2∞ in reality if you look at the set of #s between 0 and 1 and 0 and 2

or between any two continuous sets of real #s actually.

If nobody answers the supposed "paradox" by tommorow I'll explain it.

I think I'll have several co-workers call the help desk, because apparently you have too much time on your hands. :p

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Originally Posted by Cim

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Originally Posted by Pureghetto

'wtf my brain hurts'.

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Originally Posted by Cim

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Originally Posted by Pureghetto

'wtf my brain hurts'.

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Originally Posted by Flying Mullet

I think I'll have several co-workers call the help desk, because apparently you have too much time on your hands. :p

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=( they made me work 60 mins overtime and I'm already at 26 mins out of the 60.

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Originally Posted by Flying Mullet

Remember, ∞ + ∞ = ∞ and ∞ * ∞ = ∞. There's no such thing as 2∞ or something like it. Infinity is not a variable like x. Thus, the numbers between 0 and 1 are ∞ and 1 and 2 are ∞, or ∞ + ∞ = ∞.

I hope that makes sense.

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That's almost as cool as two space ships travelling towards each other with speed 0.9c relative to, say, the earth, yet their speed relative to each other is not 1.8c, but 0.99c.

Relativity = Brain Implosions :D

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Originally Posted by Little Blue

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Originally Posted by Flying Mullet

Remember, ∞ + ∞ = ∞ and ∞ * ∞ = ∞. There's no such thing as 2∞ or something like it. Infinity is not a variable like x. Thus, the numbers between 0 and 1 are ∞ and 1 and 2 are ∞, or ∞ + ∞ = ∞.

I hope that makes sense.

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That's almost as cool as two space ships travelling towards each other with speed 0.9c relative to, say, the earth, yet their speed relative to each other is not 1.8c, but 0.99c.

Relativity = Brain Implosions :D

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hint: except infinites don't work that way. "2∞" != ∞ , when using my confusing stories.

It's a similar headache-problem to the one my math teacher told me in high school:

Say you're 50 feet away from a door. You move halfway towards it, you're at 25 feet. Then 12.5 feet, etc. Eventually you'll be around .5 feet, then .25 feet, then .125 feet, etc. If you keep moving halfway, do you ever reach the door?

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Originally Posted by Little Blue

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Originally Posted by Flying Mullet

Remember, ∞ + ∞ = ∞ and ∞ * ∞ = ∞. There's no such thing as 2∞ or something like it. Infinity is not a variable like x. Thus, the numbers between 0 and 1 are ∞ and 1 and 2 are ∞, or ∞ + ∞ = ∞.

I hope that makes sense.

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That's almost as cool as two space ships travelling towards each other with speed 0.9c relative to, say, the earth, yet their speed relative to each other is not 1.8c, but 0.99c.

Relativity = Brain Implosions :D

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WHAT!?:down: :smash:

BOOM!

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Originally Posted by Raistlin

It's a similar headache-problem to the one my math teacher told me in high school:

Say you're 50 feet away from a door. You move halfway towards it, you're at 25 feet. Then 12.5 feet, etc. Eventually you'll be around .5 feet, then .25 feet, then .125 feet, etc. If you keep moving halfway, do you ever reach the door?

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Except you know that the sum of x/n where n are the integers n > 0 = 1, so you know you get to the door.

Most people aren't familiar with Calculus, though. :p

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

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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

∞
/
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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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Originally Posted by Pureghetto

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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 :)

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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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Originally Posted by o_O

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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 :(

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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!!!

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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

∞
/
_

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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

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Originally Posted by Pureghetto

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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

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Originally Posted by Raistlin

Say you're 50 feet away from a door. You move halfway towards it, you're at 25 feet. Then 12.5 feet, etc. Eventually you'll be around .5 feet, then .25 feet, then .125 feet, etc. If you keep moving halfway, do you ever reach the door?

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Yes; reach out, turn the the knob and continue on through.

mosquito elasticity is overrated...

Isn't this what transfinite numbers are about? I don't remember the details, only references to 'closed infinity' and 'open infinity'. It's still an infinite number either way, i.e. it's utterly endless, but a 'closed' definition of infinity is "all numbers between x and y" where an 'open' infinite value is simply "all numbers".

Something like that, there are people who can understand and explain this infinitely better than me.

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Originally Posted by Big D

Isn't this what transfinite numbers are about? I don't remember the details, only references to 'closed infinity' and 'open infinity'. It's still an infinite number either way, i.e. it's utterly endless, but a 'closed' definition of infinity is "all numbers between x and y" where an 'open' infinite value is simply "all numbers".

Something like that, there are people who can understand and explain this infinitely better than me.

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Laypeople explain things better than non-laypeople.

Not saying anything about you per se, but you used a layperson explanation when I could not possibly do so.

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Originally Posted by Big D

Something like that, there are people who can understand and explain this infinitely better than me.

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Boooo! :p