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6/6/2014 4:51:56 AM
43
"Some Infinities are Larger than Others"
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Well, why don't we look at it from a non-mathematical standpoint (?), for example: When we do calculations for [url=http://en.wikipedia.org/wiki/Fracture_mechanics]small cracks[/url] in a infinitely large plate, the plate doesn't actually need to be [i]that[/i] big before experimental results coincide well with our theoretical results. And yet, that "infinite" plate may be much bigger than, oh, say an electron making a U-turn in an "infinite" [url=http://sdsu-physics.org/physics180/physics180B/p180b_images/force_on_electron.gif]magnetic/electric[/url] field. That's the first two examples that came into mind, but I'm sure there are better ones. So I would say some are larger than others.
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2 답변I've got a pretty large infinity right here in my pants if you know what I mean. [spoiler]I'm sorry:([/spoiler]
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3 답변작성자: BannedPiranha 6/7/2014 3:13:20 PMTrue. There are multiple types of infinity. An infinite set of real numbers is larger than an infinite set of whole numbers.
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2 답변Infinity is really just any number it's just that infinity is usually used when you have achieved a number that is to high to count to
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2 답변Lim x -> infinity of x/(x^2) = 0. Some infinities are larger than others conceptually.
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An infinity can be larger when it raises at a faster rate: Lim x->infinity. (2x^3)/(3x^2) = infinity " ". (2x^2)/(3x^2) = 2/3 " ". (2x^2)/(3x^3) = 0 The rate that infinity increased makes a difference in relation to limits.
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2 답변Say you have a set of all real, whole numbers. It is an infinite set. Now let's say you have a set of all integers, including fractions and decimals. It is also an infinite set, but contains more values, and so is larger. I'm not too sure on the concept myself, so my explanation might be bad, but I've had it explained to me in a way that makes sense, so I know it's true
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10 답변Infinity is infinity. If i take all the even numbers in the universe then that's one infinity and if I take all the natural numbers in the universe thats another infinity. If somewhere along the line we stopped counting the even numbers, say at a billion, then it would be a shorter list than the list of natural numbers, but we don't stop counting. Ever. That's the point of infinity. Although the even number list may seem to be lagging behind the other one, you can only say that one list is shorter when you stop counting and that doesn't happen.
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