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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
Does infinite equal infinite? - Mathematics Stack Exchange All three integrals are divergent and infinite and have the regularized value zero, but two of them are equal but not equal to the third one In other cases of divergent integrals or series, the regularized value and or growth rate (germ at infinity) or behavior at a singularity can differ as well or the differences can compensate for each other as in the example above So no, at least in
Dihedral subgroup of a infinite Coxeter group I have seen a conclusion that every infinite Coxeter group contain an infinite dihedral subgroup, but I have no idea how to prove it Could anyone give me some hint?
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
Uncountable vs Countable Infinity - Mathematics Stack Exchange 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
What is the difference between infinite and transfinite? Infinite simply means "not finite", both in the colloquial sense and in the technical sense (where we first define the term "finite") There is no technical definition that I am aware of for "transfinite" Nevertheless, I can attest to my personal use Transfinite is good when there is a notion of order, so "transfinite ordinal", or when you want to talk about non-standard real numbers which
In an infinite sum, is there an actual term at an infinite position? As for what infinite summation means Zeno's first paradox maps to this very problem Infinite summation shows how an infinite number of terms can sometimes add up to a finite number Edit 2: Per a long conversation in the comments, we found that a misunderstanding about the set of natural numbers is at the heart of the confusion