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

Oct 4, 2020 · I am a little confused about how a cyclic group can be infinite. To provide an example, look at $\\langle 1\\rangle$ under the binary operation of addition. You can never make any negative …

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 …

Mar 8, 2018 · The Koch snowflake has finite area, but infinite perimeter, right? So if we make this snowflake have some thickness (like a cake or something), then it appears that you can fill it with …

A compact subset of an infinite dimensional Banach space can be infinite dimensional, in the sense that it is not contained in any finite dimensional subspace. One way to generate infinite dimensional …

Nov 7, 2022 · I see what you mean, so does a normed-space being infinite means that it maps a vector space to a continous interval? If this is the case how do we have a finite normed-space?

The dual space of an infinite-dimensional vector space is always strictly larger than the original space, so no to both questions. This was discussed on MO but I can't find the thread.

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 …

Write out a few terms of the series. You should see a pattern! But first consider the finite series: $$\sum\limits_ {n=1}^ {m}\left (\frac {1} {n}-\frac {1} {n+1 ...

Nov 15, 2024 · 1 Can it be proven using the pigeonhole principle that if set A is an uncountable family of finite sets, it contains an uncountable subfamily all of whose elements have cardinality n? The idea is …