Aug 11, 2012 · I know that $\\infty/\\infty$ is not generally defined. However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as-big infinity, for

My friend and I were discussing infinity and stuff about it and ran into some disagreements regarding countable and uncountable infinity. As far as I understand, the list of all natural numbers is

An infinite number? Kind of, because I can keep going around infinitely. However, I never actually give away that sweet. This is why people say that 1 / 0 "tends to" infinity - we can't really use infinity as a …

May 3, 2020 · How do you extend your definitions to that case, and how infinite is n n? Assuming n =N n = N, the product of two such matrices is still not always well-defined, take for instance the matrix …

In his book Analysis Vol. 1, author Terence Tao argues that while each natural number is finite, the set of natural numbers is infinite (though has not defined what infinite means yet). Using Peano...

Mar 28, 2023 · Is there any pathological shape that has a finite surface area but an infinite volume, sort of like the opposite of a Gabriel's horn?

4 If "almost infinite" makes any sense in any context, it must mean "so large that the difference to infinity doesn't matter." One example where this could be meaningful is if you have parallel resistors and …

Aug 7, 2014 · Countability is a different concept altogether. An infinite bounded set can be countable (e.g. all rationals between 0 and 1) or uncountable (e.g. all reals between 0 and 1).

Obviously it depends on the definition of "exists". Some authors explicitly work over the extended real line with ±∞ ± ∞ adjoined, so that such infinite limits do explicitly "exist" as first-class values. But …

Dec 1, 2014 · But the circumference also defines the subset with infinite area that lays "outside" (which is a conventional concept). That other "outside shape" would be an example of a finite-perimeter …