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  1. #1
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    The paradox of Infinity

    So Infinity is such a difficult concept to get my head around.


    If you count 1..2...3...4...5...6....7..8 etc you can go on forever.

    If you decide count half the numbers ie the even numbers you would still count forever so half of infinity is infinity!! This does not make sense!

  2. #2
    Secondary Hivemind Nexus Heliocentric's Avatar
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    Good talk.
    I'm failing to writing a blog, specifically about playing games the wrong way
    http://playingitwrong.wordpress.com/

  3. #3
    Secondary Hivemind Nexus Fumarole's Avatar
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    The Medallion of the Imperial Psychopath, a Napoleon: Total War AAR
    For the Emperor!, a Total War: Shogun 2: Fall of the Samurai AAR
    The Red Blades, a Battle Brothers AAR

  4. #4
    Secondary Hivemind Nexus Zephro's Avatar
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    You've sort of included the solution to the paradox in your post. The paradox arose because it was insisted there is just one thing, infinity. Until it was pointed out that you can have different infinite things that definitely don't have the same number of things. The trick is that infinity isn't a number it's a limit. It's the limit beyond which you can't assign a value anymore. If you phrase it that way it makes sense you can have 2 sets which size are beyond counting but clearly have different sizes.

  5. #5
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    Quote Originally Posted by Fumarole View Post
    That was great :) my head hurts now!

  6. #6
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    Quote Originally Posted by Zephro View Post
    You've sort of included the solution to the paradox in your post. The paradox arose because it was insisted there is just one thing, infinity. Until it was pointed out that you can have different infinite things that definitely don't have the same number of things. The trick is that infinity isn't a number it's a limit. It's the limit beyond which you can't assign a value anymore. If you phrase it that way it makes sense you can have 2 sets which size are beyond counting but clearly have different sizes.
    But it's not a limit, is it? You can just keep going.

  7. #7
    Secondary Hivemind Nexus Heliocentric's Avatar
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    No, infinity is a limit, just one that cannot be surpassed.
    I'm failing to writing a blog, specifically about playing games the wrong way
    http://playingitwrong.wordpress.com/

  8. #8
    Secondary Hivemind Nexus Zephro's Avatar
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    Quote Originally Posted by Sarfrin View Post
    But it's not a limit, is it? You can just keep going.
    In the sense that a limit is a property and not a number exactly (though it can be one). So infinity isn't a number but a property of things. E.g. if you take a set of things the limit of it's size might be infinite. Rather than being an actual number you are counting towards. So things will tend towards infinity or have no upper limit, but that doesn't make infinity a number you can actually assign or manipulate like a normal number. Which means that 2 different sets of things tending to infinity can have different sizes.

    It's the difference between saying "this list just keeps on going forever" and "the list has a size of X and X is the infinity number".

  9. #9
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    I get the idea that infinity isn't a number. I can also see how two infinite sets can contain different numbers of things. It's just the idea of infinity as a limit that doesn't limit anything, but maybe that's a semantic thing.

  10. #10
    Secondary Hivemind Nexus Gus_Smedstad's Avatar
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    There's a concept in mathematics of a "limit" to a function. This is the value that the function approaches but never reaches as X approaches some value. The limit of f(x) can apply to any value of X, but one common value is infinity.

    For example, suppose f(x) = 1/x. The limit of f(x) as x approaches infinity is 0, but it's never actually zero for any finite value, just a very small value. Conversely, as long as we're tossing around infinity and limits, f(0) = 1/0 is an undefined value, but the limit of f(x) as x approaches 0 is infinity.

    Limits are highly useful things, since we get things like calculus from limits.

  11. #11
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    So yes, mathematical meaning is subtly different from the common one. I stopped learning maths before calculus came into the syllabus and haven't had a big enough incentive to learn it since. I am mildly curious about it though.

  12. #12
    Lesser Hivemind Node Matt_W's Avatar
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    There's also some confusion because infinity doesn't actually exist. All things are countable, so an actual countable number can be assigned to any real problem or situation, even those with probabilities, which probably have the largest numbers we can conceive of. Infinity functions as an abstraction, an estimate. It indicates that I can replace the "infinite" quantity with any other arbitrarily large one. I often say things like "from the point of view of that (very fast) circuit, a second is effectively an infinite length of time." All this means is that it doesn't matter if we're talking about 1 second or 10 seconds or a year; the behavior of the circuit would be the same.

  13. #13
    Secondary Hivemind Nexus Heliocentric's Avatar
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    Infinity might exist, space or time might be infinitive for example, but it mightn't.
    I'm failing to writing a blog, specifically about playing games the wrong way
    http://playingitwrong.wordpress.com/

  14. #14
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    The only way we can find out is to boldly go there.

  15. #15
    Secondary Hivemind Nexus Zephro's Avatar
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    Quote Originally Posted by Sarfrin View Post
    So yes, mathematical meaning is subtly different from the common one. I stopped learning maths before calculus came into the syllabus and haven't had a big enough incentive to learn it since. I am mildly curious about it though.
    That's the nub of the thing. The paradox only exists the moment you try to do maths with the common concept of infinity. Then once you slot in the more technical difference the paradox is solved. It's weirdly true of a lot of things in life, where taking every day descriptions into maths/science/philosophy/logic they all break, or taking the "accurate" descriptions back into pub talk stops making any sense. An example of the reverse is eating peanuts in the pub and somebody pointing out they are in fact not nuts. Which is taking a specific botanical factual meaning of the word nut and applying it to a context where it makes no sense. In the context of a pub a peanut is a fucking nut, it's not somehow more intelligent to say otherwise.

  16. #16
    Secondary Hivemind Nexus Heliocentric's Avatar
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    Quote Originally Posted by Zephro View Post
    In the context of a pub a peanut is a fucking nut, it's not somehow more intelligent to say otherwise.
    You are nuts.
    I'm failing to writing a blog, specifically about playing games the wrong way
    http://playingitwrong.wordpress.com/

  17. #17
    Secondary Hivemind Nexus Gus_Smedstad's Avatar
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    Quote Originally Posted by Heliocentric View Post
    You are nuts.
    Careful. Say that in a pub and you might get a whack to the nuts.

  18. #18
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    Technically, they're not actually nuts.

  19. #19
    Lesser Hivemind Node Matt_W's Avatar
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    Quote Originally Posted by Heliocentric View Post
    Infinity might exist, space or time might be infinitive for example, but it mightn't.
    That's kind of the point though. Any measurement we make or perception that we can actually have is bounded in time and space. Anything outside that is irrelevant. It might be that all the space just outside the visible universe is filled with packing peanuts.

    Quote Originally Posted by Sarfrin View Post
    Technically, they're not actually nuts.
    WHACK!

  20. #20
    Secondary Hivemind Nexus BillButNotBen's Avatar
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    Quote Originally Posted by Sarfrin View Post
    Technically, they're not actually nuts.
    Technically, they're not actually peas.

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