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  1. How can I define $e^x$ as the value of infinite series?

    Are you familiar with Taylor series? Series solutions of differential equations at regular points? From what foundation/background are you approaching this problem?

  2. Infinite monkey theorem and numbers - Mathematics Stack …

    Mar 15, 2021 · 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 …

  3. 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...

  4. 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 …

  5. real analysis - Meaning of Infinite Union/Intersection of sets ...

    Meaning of Infinite Union/Intersection of sets Ask Question Asked 8 years, 8 months ago Modified 4 years, 1 month ago

  6. elementary set theory - What do finite, infinite, countable, not ...

    What do finite, infinite, countable, not countable, countably infinite mean? [duplicate] Ask Question Asked 13 years, 2 months ago Modified 13 years, 2 months ago

  7. Infinite class of closed sets whose union is not closed

    Aug 4, 2016 · 0 Since singletons in R are closed in usual topology. We can think about infinite class of singletons {x} where x belongs to (0,1] then there union will be (0,1] which is not …

  8. linear algebra - What, exactly, does it take to make an infinite ...

    Oct 31, 2017 · Hence a vector space is infinite dimensional iff it has a basis which is infinite. If your infinite dimensional space has an inner product and is complete with respect to the …

  9. One divided by Infinity? - Mathematics Stack Exchange

    Infinite decimals are introduced very loosely in secondary education and the subtleties are not always fully grasped until arriving at university. By the way, there is a group of very strict …

  10. Questions about the Infinite Monkey Theorem - Mathematics …

    Nov 15, 2023 · (Context: the Infinite Monkey Theorem stipulates that given infinite time, a monkey can type out the complete works of Shakespeare, or any other text of finite length, just by …