Quote :

"Terms like more and less don't even apply to the concept of infinity."

perhaps i am wrong in my statement

10/15/2009 7:24:42 PM

yes, you are

10/15/2009 7:28:17 PM

To TreeTwista's credit though, he is right if you restrict your notion of infinity.

If you're talking about just countable infinity (the same size as the natural numbers), then there's no notion of "more" or "less" of it. Either it's countably infinite, or it's not. There are as many primes as natural numbers, as many even numbers as naturals, as many numbers divisible by 3, etc.

10/15/2009 7:41:21 PM

i don't think they covered non-countable infinities in MA242 or ST311 which is as far as I got

10/15/2009 7:53:17 PM

You just don't see them explicitly. You're dealing with an uncountably infinite set whenever you're dealing with an interval of real numbers. You see these in calculus all the time (bounds of integrals).

You usually only see the higher orders of infinity if you have a set theory course, or maybe a computability-theory course. Those are things that only philosophers, mathematicians, and computer scientists normally take.

10/15/2009 8:03:36 PM

Hey, get out of here Mcdanger, im the resident mathematician

10/15/2009 9:07:01 PM

you know i LOVE conversations like this

because it makes me sit here and actually think about it.
because i can't comprehend it at first.


awesome.

10/15/2009 9:09:17 PM

Resident Mathematician Battle

1985 vs McDanger

Math Knowledge - Verdict: Tossup

Screenname - Verdict: 1985

i mean his SN is all numbers

10/15/2009 9:09:47 PM

Quote :

"There are varying degrees of infinite, each of which differ infinitely in magnitude."

This is true. There are, in fact, infinity infinities. What's more, the infinity defined by the quantity of the infinities is greater than every single one of those individual infinities. No shit.

You're not even allowed to put all the infinities into a single set...chaos ensues if you do

10/15/2009 9:17:26 PM

Its turtles, all the way down

10/15/2009 9:20:44 PM

Quote :

"There are as many primes as natural numbers,"

there exists proof against this right. Mersenne's theory is based upon the very idea that primes become more sparse the larger the number
http://www.thefreelibrary.com/Zeroing+in+on+an+infinite+number+of+primes.-a021282798

and it's been discussed how there are some infinities that by their existence must be less than other infinities what with the aleph naught and all. how can you not use one to disprove the other

10/15/2009 9:26:28 PM

ive said it before and I'll say it again,
there is always a prime between N and 2N

10/15/2009 9:29:07 PM

What's all this, then? You people can't go having a math thread without me.

10/15/2009 11:12:14 PM

no numbers in your name shadowrunner, let alone your sn isnt all numbers

ADVANTAGE 1985

10/15/2009 11:15:09 PM

naw, I can math it up with the best of them, son. i've got numbers in my blood, son.

10/15/2009 11:27:38 PM

Quote :

"Hey, get out of here Mcdanger, im the resident mathematician"

*breaks out the turn tables*

Quote :

"Resident Mathematician Battle 1985 vs McDanger Math Knowledge - Verdict: Tossup Screenname - Verdict: 1985 i mean his SN is all numbers"

fuck.

Quote :

"This is true. There are, in fact, infinity infinities. What's more, the infinity defined by the quantity of the infinities is greater than every single one of those individual infinities. No shit."

You can do arithmetic with transfinite ordinals. Here's what happens when you raise countable infinity to countable infinity:




Picture seems confusing at first, but keep in mind each converging sequence is meant to represent a copy of the natural numbers. Each turn of the spiral is a power of omega (the size of the natural numbers).

[Edited on October 18, 2009 at 12:22 PM. Reason : .]

10/18/2009 12:20:39 PM

^ perhaps im reading you wrong, but a countably infinite collection of countably infinities is still just countably infinite. Consider the infinite sets {A}, {B}, {C} ,{D}...

A bijection X from N to all of the members of these infinities is
X1 = A1, X2 = B2, X3=A2, X4 = B2, X5 = C1... etc

10/18/2009 12:50:02 PM

this thread freaking rocks

10/18/2009 1:16:07 PM

Quote :

"^ perhaps im reading you wrong, but a countably infinite collection of countably infinities is still just countably infinite. Consider the infinite sets {A}, {B}, {C} ,{D}... A bijection X from N to all of the members of these infinities is X1 = A1, X2 = B2, X3=A2, X4 = B2, X5 = C1... etc"

Yeah I agree with what you've said. I'm not sure what about what I said that you're misinterpreting.

[Edited on October 18, 2009 at 4:04 PM. Reason : .]

10/18/2009 4:03:08 PM

Polar coordinates, A={(1,n):n=0,1,2,3...., n in radians}. F is a rotation of 1 radian counter clockwise about the origin. It's been over a week; just in case anyone's still wondering about that isometry shit.

10/25/2009 6:30:45 AM

Infinite is counterintuitive to the human mind.

10/25/2009 6:53:40 AM