What is the difference between 1 divided by 0 or both?
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I don't know what it is called.Would it be 1 if we had 2 equal infinities divided by each other?
Would we get 2 if we had an infinite divided by a half-as-big one?For example, how about $frac1+1+ldots2+2+
You gave the answer, and it's not just because it should be the result of limiting processes of different nature.The definition would be given for completeness and coherence with the fact that the limiting ratio is the ratio of the limits.
People who aren't mathematicians ask me, "You know math, huh?"I can only reply, "The words you just uttered do not make sense."That wasn't a mathematical sentence.You said that it was like a number.It is not.I don't know what truth is divided by beauty.I can divide numbers.Those are not numbers.
There are at least two different approaches to the issue of infinite/infinity in math.
There is an indeterminate form.One is interested in the behavior of the ratio of two expressions, which are both increasing without bound, as their common parameters "tend" to its limiting values.
In an enriched number system containing both infinite numbers and infinitesimals, one can avoid discussing things like indeterminate forms and tending, and treat the question purely algebraically.
One advantage of approach (2) is that it allows one to discuss indeterminate forms in concrete fashion and distinguish several cases depending on the nature of numerator and denominator: infinitesimal, infinite, or appreciable finite, before discussing the technical notion of limit which tends to be confusing to beginners.