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What exactly is infiniteby MightyKaykoher
Tags: infinite 
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#19
Jan1214, 01:37 PM

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#20
Jan1214, 01:40 PM

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I know lavinia, but they're not part of the real numbers, and the usage of statements like "inf  inf = 0" strongly suggests to me that the OP is not ready to be introduced to the mathematical details without a conceptual understanding of why infinity can not be treated that way without additional tools.



#21
Jan1214, 02:30 PM

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#22
Jan1214, 02:38 PM

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Assuming infinities to be equal does not mean they have to be finite. I would like to know how you came to that conclusion. For example, we know that there are an equal number of real numbers and irrational numbers, and both of these sets are infinite in cardinality. inf  inf is undefined because you run into problems defining inf + inf (or subtraction) and retaining distributive/associative laws, and other field axioms (even though an extension to infinity technically isn't a field (afaik) we would still want to keep it as "fieldlike" as possible and retain these simple properties.) No operation on infinity would be left undefined just because of some "well infinity is super weird," copout explanation, it would be left undefined because we can't find a way to define it without coming up with undesirable consequences, and that is all. Operations work with whatever the hell we want them to as long as our definition of those operations are consistent. Infinity * Infinity is not like Infinity  Infinity. We can define it just fine and run into absolutely no problems whatsoever. Real Projective Line The only reason we say "limit as n approached infinty 1/n" in the real numbers is because infinity is not in the set of real numbers. Once we add points for infinity in the extended real line, 1/infinity means exactly the same thing as the limit. We don't even have to do anything to say that 1/infinity = 0 after extending the real line. Furthermore, there is no reason to confine the discussion to the context of the real number line. The real number line is not the "one, true, number system." Your opinion of the real number line seems almost similar to the opinion of some ancient mathematicians' opinion of the natural numbers. I see a lot of people say that "##1/0## is meaningless because it is not defined in the real number line." No, it's not meaningless, it is meaningless in the context of the real number line because it is not defined in the real number line, in the same way that ##327## is meaningless and undefined in the natural numbers. The moment we start talking about operations on infinity, we are extending the real number line. It is not useful to stay in the real numbers. Your post saying that everything involving infinity is undefined because it is not a real number is no different than me going into the Math Homework forum and telling everyone that involves complex numbers in their work that their entire assignment is undefined and makes no sense because complex numbers are not real numbers. We can define complex numbers consistently, and so we can work with them. We can define operations on infinity consistently, so we can work with them. Infinity  R = Infinity In any extension. Infinity * R = Infinity Where R is not zero in the projective real line. In the extended real line, infinity is signed, and so this operation changes in the expected and natural way in the extended real line. Yes, an infinite amount of energy is required for a massive particle to reach the speed of light. What do you mean, "wait what? how much is infinite?" You seem to be expressing some sort of problem with the idea that an infinite amount of energy is required for a massive particle to reach the speed of light. That is true (afaik) according to very sound modern physics.. 


#23
Jan1214, 03:04 PM

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Hey 1mile, I believe what the poster you're replying to was trying to convey the notation of infinite cardinalities coming in different magnitudes and conveying different information, but I could have read too much into it.



#24
Jan1214, 03:11 PM

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It is no problem, I very much appreciate his post.



#25
Jan1214, 03:21 PM

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I don't see anything in that user's post reflecting that idea, I took the relevant part his post to mean that I don't know that ∞ = ∞. 


#26
Jan1214, 05:46 PM

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I'm still missing something.
Infinity can be put into a variable. Let's call it a. a  4..... It's simplified. If infinity is a concept then why does it appear in real life situations. Inf^2 okay, my understanding of this statement is there is this limitless number ( not a mathmatical limit ) and this strange irrational endless number is multiplied by itself. I believe in no real life situation does infinity^2 EVER happen so no use going any farther. Inf  inf = 0. Okay so, we don't know what infinite is, but infinite = infinite in all cases. Here's an inequality that IS true infinite  (positive C) < infinite. If this paragraph is completely wrong then infinite does not equal infinite. If inf  inf = 0 then inf  C must be less than infinity. Why? Who knows!! Infinite * 2 is 2infinity. If not then infinite^n * Real number (plus or minus c) is infinity. This makes no sense however this isn't how infinity shows up in real life. Infinite/infinite this is in fact 1 1/0 = infinity but, 0 times infinite equals 0. This means you can divide one into as many groups of zero as you want. Until you reach infinity groups.( this will never happen ). Why is zero times infinite 0? Well 0 + 0 + 0... Will never reach the sum of a number > 0. Infinite + C. Just the inverse of inf  C. How about the square root of infinity. That's a tough answer 


#27
Jan1214, 06:04 PM

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#28
Jan1214, 06:21 PM

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#29
Jan1214, 06:28 PM

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#30
Jan1414, 09:42 PM

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Infinite occurs in real life. Look up the definition of infinity on Wikipedia. ;



#31
Jan1414, 10:02 PM

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You keep refusing to actually give any meaningful example of what you think is infinite in the real world. This is getting old. 


#32
Jan1414, 10:43 PM

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#33
Jan1514, 01:58 AM

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As the original question has been asked and answered I am closing this thread. 


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