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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
Proof of infinite monkey theorem. - Mathematics Stack Exchange The infinite monkey theorem states that if you have an infinite number of monkeys each hitting keys at random on typewriter keyboards then, with probability 1, one of them will type the complete works of William Shakespeare
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
Types of infinity - Mathematics Stack Exchange Not only infinite - it's "so big" that there is no infinite set so large as the collection of all types of infinity (in Set Theoretic terms, the collection of all types of infinity is a class, not a set) You can easily see that there are infinite types of infinity via Cantor's theorem which shows that given a set A, its power set P (A) is strictly larger in terms of infinite size (the
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
Subspaces of an infinite dimensional vector space If V V is an infinite dimensional vector spaces, then it has an infinite basis Any proper subset of that basis spans a proper subspace whose dimension is the cardinality of the subset So, since an infinite set has both finite and infinite subsets, every infinite dimensional vector space has both finite and infinite proper subspaces
What is imaginary infinity, $i\\lim\\limits_{x \\to \\infty} x = i\\infty$? So −∞ ∞ indicates infinite magnitude- negative parity Non-zero Complex numbers do not have a single bidirectional parity A complex number has two components, a real one and an imaginary on and thus are two-dimensional and instead of having a single positive negative parity, they have a directional angle called an argument