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  1. infinity - What is the definition of an infinite sequence ...

    2024年5月12日 · 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 …

  2. Proof of infinite monkey theorem. - Mathematics Stack Exchange

    2015年4月24日 · 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 …

  3. elementary set theory - What is the definition for an infinite set ...

    2020年12月3日 · 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 …

  4. Infinite monkey theorem and numbers - Mathematics Stack …

    2021年3月15日 · I had a discussion with a friend about the monkey infinite theorem, the theorem says that a monkey typing randomly on a keyboard will almost surely produce any given books …

  5. Given an infinite number of monkeys and an infinite amount of …

    2011年1月12日 · I doubt an infinite number of monkeys could even put together a full page full of nonsense but reasonable-length words with punctuation. You could ask the same question …

  6. general topology - Why is the infinite sphere contractible ...

    Why is the infinite sphere contractible? I know a proof from Hatcher p. 88, but I don't understand how this is possible. I really understand the statement and the proof, but in my imagination this...

  7. Types of infinity - Mathematics Stack Exchange

    2012年12月18日 · 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 …

  8. linear algebra - Definition of Infinite Dimensional Vector Space ...

    2020年9月24日 · In the text i am referring for Linear Algebra , following definition for Infinite dimensional vector space is given . The Vector Space V(F) is said to be infinite dimensional …

  9. calculus - Infinite Geometric Series Formula Derivation

    Infinite Geometric Series Formula Derivation Ask Question Asked 12 years, 8 months ago Modified 4 years, 11 months ago

  10. 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 …