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(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
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
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
functional analysis - Where can I find the paper Un théorème de . . . J P Aubin, Un théorème de compacité, C R Acad Sc Paris, 256 (1963), pp 5042–5044 It seems this paper is the origin of the "famous" Aubin–Lions lemma This lemma is proved, for example, here and here, but I'd like to read the original work of Aubin However, all I got is only a brief review (from MathSciNet)
Homotopy groups U(N) and SU(N): $\\pi_m(U(N))=\\pi_m(SU(N))$ As for your request regarding a table of the homotopy groups of SU(N) S U (N), the groups πm(SU(N)) π m (S U (N)) for 1 ≤ m ≤ 15 1 ≤ m ≤ 15 and 1 ≤ N ≤ 8 1 ≤ N ≤ 8 are given in appendix A, section 6, part VII of the Encyclopedic Dictionary of Mathematics This doesn't quite cover all the cases you asked for in the comment below, but the missing ones follow from complex Bott