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Posted: 3/28/2006 7:13:14 PM EDT
[Last Edit: 3/28/2006 7:13:51 PM EDT by Greenhorn]
I was playing CoD 2, and I got a score of 2-0 (short game), and I realized, the ratio of kills to deaths is infinite. I don't have 100,000,000,000 times more kills than deaths, or 1x10^100,000,000,000. It's infinite.

Well, what if I got 3-0? That's an infinite ratio too, but 3 is greater than 2, so it must be a different infinity, right?

This is along the lines of "is .9bar = 1?"

I'm bored.

Link Posted: 3/28/2006 7:14:56 PM EDT
[Last Edit: 3/28/2006 7:15:22 PM EDT by DK-Prof]
I learned that there are many types of infinity years ago from listening to the commentary for Futurama. A lot of the writers on that show were apparently huge math nerds.

Link Posted: 3/28/2006 7:15:15 PM EDT
Link Posted: 3/28/2006 7:16:13 PM EDT
you've never gotten into an argument with an 8 year old?


no times infinity!

yes times infinity times ten!

no times infinity times a million!

yes times infinity times infinity!
Link Posted: 3/28/2006 7:21:11 PM EDT
If you want to find out which infinity is bigger, divide them. Which is bigger, 3/0 or 2/0?

(3/0)/(2/0) = 3/2. Therefore 3/0 is 1.5 times bigger than 2/0. (If using zero blows your mind, use n and then see what the value is as n approaches zero).
Link Posted: 3/28/2006 7:21:30 PM EDT

Originally Posted By Greenhorn:
I was playing CoD 2, and I got a score of 2-0 (short game), and I realized, the ratio of kills to deaths is infinite. I don't have 100,000,000,000 times more kills than deaths, or 1x10^100,000,000,000. It's infinite.

Well, what if I got 3-0? That's an infinite ratio too, but 3 is greater than 2, so it must be a different infinity, right?

This is along the lines of "is .9bar = 1?"

I'm bored.




3-0 is not infinity, it's just not defined.

Now, there's countable infinity (i.e. the infinity of the natural numbers 1,2,3,4.....etc).


There's the infinity of the real numbers, which is the number of points between 0 and 1.

The latter is much bigger than the former; and there's infinitely many infinitites between them.


Head spinning yet?
Link Posted: 3/28/2006 7:22:12 PM EDT

Originally Posted By Greenhorn:
I was playing CoD 2, and I got a score of 2-0 (short game), and I realized, the ratio of kills to deaths is infinite. I don't have 100,000,000,000 times more kills than deaths, or 1x10^100,000,000,000. It's infinite.

Well, what if I got 3-0? That's an infinite ratio too, but 3 is greater than 2, so it must be a different infinity, right?

This is along the lines of "is .9bar = 1?"

I'm bored.




You are bored indeed.
Link Posted: 3/28/2006 7:23:38 PM EDT
There are at least two types of infinity. I even taught my mother how to prove it on one piece of paper.

I had a girlfriend of several years break up with me because she didn't believe me about different sizes of infinity. She thought I was just making it up to make myself seem smart and exacerbate her inferiority complex.

Two kinds are: the number of counting numbers and the number of points on a line.
Link Posted: 3/28/2006 7:26:42 PM EDT
Aleph numbers, ordinal infinite sets.... there are infinite infinities
Link Posted: 3/28/2006 7:27:27 PM EDT

Originally Posted By DoubleFeed:
Infinity cannot be quantified.



Sure it can! (well, some of them)

There are, if I'm remembering my math class days correctly, two types of mathematical infinites.

The "countable infinites" can be expressed in some fashion that completely describes a set with infinite members. The set of all integers is infinite, but we can express them {1, 2, 3, ... n, n+1... }. We can also express all rational numbers, because they're a ratio of two integers. {all m/n, such that m, n are integers } Both integers and rational numbers are infinite, because for every interger n there is an n+1, and for every ratio m/n there is a ratio m+1/n, m+1/n+1, and m/n+1.

The "uncountable infinites" cannot be expressed in any complete fashion. The set of all real numbers is uncountable, because for any two rational numbers you could possibly pick to express adjacent values, there are an infinite number of values in the set between them. You could try to count n + 0.(BIGNUMBER of 9's), n+1, and you'd be missing an infinite number of real values in between.

Just because an infinite is countable or uncountable, doesn't make one bigger or smaller. Infinites have no proportional size relative to each other. Countable infinites have some properties so that set theorists can work with them, while uncountables don't.

Link Posted: 3/28/2006 7:33:33 PM EDT

Originally Posted By Horseman:

Originally Posted By DoubleFeed:
Infinity cannot be quantified.



Sure it can! (well, some of them)

There are, if I'm remembering my math class days correctly, two types of mathematical infinites.

The "countable infinites" can be expressed in some fashion that completely describes a set with infinite members. The set of all integers is infinite, but we can express them {1, 2, 3, ... n, n+1... }. We can also express all rational numbers, because they're a ratio of two integers. {all m/n, such that m, n are integers } Both integers and rational numbers are infinite, because for every interger n there is an n+1, and for every ratio m/n there is a ratio m+1/n, m+1/n+1, and m/n+1.

The "uncountable infinites" cannot be expressed in any complete fashion. The set of all real numbers is uncountable, because for any two rational numbers you could possibly pick to express adjacent values, there are an infinite number of values in the set between them. You could try to count n + 0.(BIGNUMBER of 9's), n+1, and you'd be missing an infinite number of real values in between.

Just because an infinite is countable or uncountable, doesn't make one bigger or smaller. Infinites have no proportional size relative to each other. Countable infinites have some properties so that set theorists can work with them, while uncountables don't.




This may be, but the answer IS 42.
Link Posted: 3/28/2006 7:36:17 PM EDT
There is a finite number of Infinities G35, M35, M45 and so on.......................

You will find that approaching an M series is infinitely more difficult than approaching a G infinity monetarily

The number of portals contained in said infinity is inversely proportional to the perceived sportiness of the infinity

Did that blow your mind
Link Posted: 3/28/2006 7:36:30 PM EDT
if i can drive my car at the speed of light and then turn on the headlights...what happens?
Link Posted: 3/28/2006 7:37:20 PM EDT
Cantor's set theory.
Link Posted: 3/28/2006 7:37:35 PM EDT

Originally Posted By Horseman:

Originally Posted By DoubleFeed:
Infinity cannot be quantified.



Sure it can! (well, some of them)

There are, if I'm remembering my math class days correctly, two types of mathematical infinites.

The "countable infinites" can be expressed in some fashion that completely describes a set with infinite members. The set of all integers is infinite, but we can express them {1, 2, 3, ... n, n+1... }. We can also express all rational numbers, because they're a ratio of two integers. {all m/n, such that m, n are integers } Both integers and rational numbers are infinite, because for every interger n there is an n+1, and for every ratio m/n there is a ratio m+1/n, m+1/n+1, and m/n+1.

The "uncountable infinites" cannot be expressed in any complete fashion. The set of all real numbers is uncountable, because for any two rational numbers you could possibly pick to express adjacent values, there are an infinite number of values in the set between them. You could try to count n + 0.(BIGNUMBER of 9's), n+1, and you'd be missing an infinite number of real values in between.

Just because an infinite is countable or uncountable, doesn't make one bigger or smaller. Infinites have no proportional size relative to each other. Countable infinites have some properties so that set theorists can work with them, while uncountables don't.




Yes, you can compare infinities by giving an injection or surjection. E.g., there's an injection from N to R, but not conversely, so the cardinality of the reals is larger than countable infinity.
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