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- Mathematics Stack Exchange
Q A for people studying math at any level and professionals in related fields
- (Un-)Countable union of open sets - Mathematics Stack Exchange
A remark: regardless of whether it is true that an infinite union or intersection of open sets is open, when you have a property that holds for every finite collection of sets (in this case, the union or intersection of any finite collection of open sets is open) the validity of the property for an infinite collection doesn't follow from that In other words, induction helps you prove a
- Mnemonic for Integration by Parts formula? - Mathematics Stack Exchange
The Integration by Parts formula may be stated as: $$\\int uv' = uv - \\int u'v $$ I wonder if anyone has a clever mnemonic for the above formula What I often do is to derive it from the Product R
- Expectation of Minimum of $n$ i. i. d. uniform random variables.
You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
- How do we calculate factorials for numbers with decimal places?
I was playing with my calculator when I tried 1 5! 1 5! It came out to be 1 32934038817 1 32934038817 Now my question is that isn't factorial for natural numbers only? Like 2! 2! is 2 × 1 2 × 1, but how do we express 1 5! 1 5! like this?
- The sequence of integers - Mathematics Stack Exchange
Prove that the sequence $\\{1, 11, 111, 1111, \\ldots\\}$ will contain two numbers whose difference is a multiple of $2017$ I have been computing some of the immediate multiples of $2017$ to see how
- Prove that the sequence (1+1 n)^n is convergent [duplicate]
It is hard to avoid "the concept of calculus" since limits and convergent sequences are a part of that concept On the other hand, it would help to specify what tools you're happy with using, since this result is used in developing some of them (For example, if you define ex = limn → ∞(1 + x n)n, then clearly we should not be using ex in the process of showing that this limit exists )
- $\\operatorname{Aut}(\\mathbb Z_n)$ is isomorphic to $U_n$.
It might be using ring theory in a non-essential way, but it is conceptually simpler because the endomorphisms are easier to describe than the automorphisms, and since the invertible elements of Zn Z n are by definition Un U n, we obtain the result without having to understand what Un U n actually looks like
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