Also, you can visualize it like this. For a slope y/x, 1/1 is a 45 degree line and, as x increases while y remains constant, the line becomes more an more horizontal, but never perfectly horizontal, where it has no slope. That is, "as x [increases] towards infinity."
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Anonymous2010-11-30 21:58
\infty is not an element of the reals, so arithmetic on it is meaningless.
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Anonymous2010-12-04 21:54
I agree with >>7 infinity is a concept. It isn't 1,2,3,1e99 it's every number possible. Actually 1/∞ = 0 can equal any number OTHER then 0 because if the value for infinity is 0 then the relation is undefined.
I once read a book called Infinity and the Mind wherein the author described "transfinite numbers". These were numbers that denoted degrees of infinity. The author used one-to-one correspondence to explain his idea of which infinite sets were the same or of a different degree (or deepness) of infinity. I recall that he basically mentioned what he thought of as two degrees of infinity (so far): numerical & spacial. He denoted one as alef 0 & the other alef 1 (sorry, I don't know how to type the appropriate Hebrew letter for "alef"). Unfortunately, I can't remember which one was the lesser infinity (alef 0) or the greater infinity (alef 1). Also, I don't recall if he had any ideas on what the next deeper level of infinity was (alef 2). So, if you replace 1/infinity with 1/alef(subscript n), you might be able to reason that the answer would be that degree of infinity denoted by alef(subscript 1/n): 1/alef n = alef (1/n) with the case that if n=0, then the answer is the lowest level of infinity, alef 0. You may all have fun ripping this apart or ignoring it as you wish!