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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
infinity - What is the definition of an infinite sequence . . . Except for $0$ every element in this sequence has both a next and previous element However, we have an infinite amount of elements between $0$ and $\omega$, which makes it different from a classical infinite sequence So what exactly makes an infinite sequence an infinite sequence? Are the examples I gave even infinite sequences?
elementary set theory - What is the definition for an infinite set . . . However, while Dedekind-infinite implies your notion even without the Axiom of Choice, your definition does not imply Dedekind-infinite if we do not have the Axiom of Choice at hand: your definition is what is called a "weakly Dedekind-infinite set", and it sits somewhere between Dedekind-infinite and finite; that is, if a set is Dedekind
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
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
I have learned that 1 0 is infinity, why isnt it minus infinity? 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 number, we can only imagine what we are getting closer to as we move in the direction of infinity