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What is infinity divided by infinity? - Mathematics Stack Exchange 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
Finding a basis of an infinite-dimensional vector space? The other day, my teacher was talking infinite-dimensional vector spaces and complications that arise when trying to find a basis for those He mentioned that it's been proven that some (or all, do
elementary set theory - What do finite, infinite, countable, not . . . A set A A is infinite, if it is not finite The term countable is somewhat ambiguous (1) I would say that countable and countably infinite are the same That is, a set A A is countable (countably infinite) if there exists a bijection between A A and N N (2) Other people would define countable to be finite or in bijection with N N
What is the difference between infinite and transfinite? The reason being, especially in the non-standard analysis case, that "infinite number" is sort of awkward and can make people think about ∞ ∞ or infinite cardinals somehow, which may be giving the wrong impression But "transfinite number" sends, to me, a somewhat clearer message that there is a particular context in which the term takes place
Is there a shape with infinite area but finite perimeter? 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 curve with an infinite area That sounds like cheating and playing with words