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Quote by: ZNFYRH  iclaudius,
I see what you're saying. Infinity is more of a limit and representation and not so much a value, right? |
Uh... no. An infinte number, most simply, is a number that is not finite. Infinity, a commonly misunderstood word, is just the quality of being infinite. When you say, "numbers go on to infinity," you're saying is that finite value can be counted, but that the actual value of everything is infinite, meaning you can't ever be finished counting, because you can always count 1 higher than what you've counted. The value of everything is not countable by finite value. That's all you're saying. In common usage, you might hear, "infinity, that means it goes on forever," but that's only half true. Yes, if you were counting finite numbers to infinity, you would be counting forever, but that doesn't mean that infinity is a number that keeps getting larger... it's just a quality. Infinity is not one "largest number." It's a type of number.
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On the division of INF by INF, I always look at it as saying, "How many times does everything go into everything?" Then again, I'm not talking about the varying "sets" of infinity.
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But that's not what infinity is. Ask yourself this: how many times does finity go into finity? We don't know! Be more specific.
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I think this relates to my perception of infinity. I think of infinity as everything. So to speak it out... "How many times does nothing go into nothing?" or "How many empty sets are in an empty set?"
On your evaluation of the equation, I also understand. People assume, as I do, that INF/INF is 1. You're saying that it isn't, and therefore the equation is invalid.
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A singular representation of all numeric value and the quality of being infinite (infinity) are not the same thing.
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I absolutely agree with this. I went to the same system of schooling as another member here who said the same thing.
I never understood how people could think something could become nothing, especially when those same people would say "matter cannot be destroyed". Yet by saying x/INF = 0 they were basically implying that it was possible.
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Well, actually, matter can be destroyed. It is converted to energy in nuclear reactions.
That aside, that particular law of physics is not strictly applicable here...