The theorem that $\binom {n} {k} = \frac {n!} {k! (n-k)!}$ already assumes $0!$ is defined to be $1$. Otherwise this would be restricted to $0 <k < n$. A reason that we do define $0!$ to be $1$ is so that …

What I would say is that you can multiply any non-zero number by infinity and get either infinity or negative infinity as long as it isn't used in any mathematical proof. Because multiplying by infinity is …

Oct 3, 2018 · As an example, I downloaded some GPS data from my camera the other day in which I found numbers like $4215.983.$ This turned out to represent $42$ degrees and $15.983$ minutes. If …

4 days ago · The question is regarding the Axiom of Choice which I am still struggling to understand; why it works and why it needs to exist. If we are given an open set X of the reals, (0,1) for example, …

Mar 28, 2022 · António Manuel Martins claims (@44:41 of his lecture &quot;Fonseca on Signs&quot;) that the origin of what is now called the correspondence theory of truth, Veritas est adæquatio rei et …

Nov 23, 2025 · The main criteria is that it be asked in bad faith. ;-). I'm not entirely insincere: The question is rather how can we tell that, and a big part of the answer is "context"; it's not mainly the …

Jan 6, 2026 · In general, people don't confuse the means with the ends. Instead, what happens is that people get so wrapped up in the means that they fail to see that the means aren't accomplishing the …

Dec 17, 2023 · The cases a and b are invalid by restrictions 1 and 2. The case c by restriction 3. PS: about “to split a DGGS cell”, for an exact definition, see DGGS standards or this animation. About …

Oct 26, 2012 · What's the difference between Fourier transformations and Fourier Series? Are they the same, where a transformation is just used when its applied (i.e. not used in pure mathematics)?

Sep 18, 2021 · In a linear algebra book, I find the term &quot;nontrivial solution&quot; and can not understand what that means. Could someone please explain what this means?