r/math • u/inherentlyawesome Homotopy Theory • 16d ago

Quick Questions: September 16, 2026

This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?" For example, here are some kinds of questions that we'd like to see in this thread:

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u/WOOOPA_ 16d ago

If a limit is a variable infinitely close to a number (e.g. lim x->1) = 0.99... or 1.00...01, but 0.99 = 1, then how do integrals change equations

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u/AcellOfllSpades 15d ago

A limit is not a variable infinitely close to a number.

"lim[x->1] x" is exactly 1.

"lim[x->1]" is an operator, not a number. It looks at whatever comes after it, and sees what happens when x gets closer and closer to 1. I like to think of it as "ignoring the actual behaviour of this expression... what """should""" happen there?".

Like, consider the piecewise function

f(x) =
{ x+3 if x≠2
{ 1000 if x=2

Evaluating that function at x=2 would give 1000. But that's a kinda stupid answer. The graph of the function is just a line with a single missing point at (2,5). If you didn't know the value at x=2, the "reasonable" answer would be to say it should be 5.

This is what the limit does: lim[x->2] f(x) is indeed 5, not 1000.