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 …

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 …

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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 …

Oct 4, 2024 · I had a teacher who mentioned in passing that Kant never read Aristotle. I've also heard this on other occasions. Did Kant actually read Aristotle or did he just become aware of it indirectly …

Feb 26, 2026 · A metric space $X$ has Property $S$ if for every $\\epsilon &gt; 0$ there is a finite cover of $X$ by connected sets with diameters $&lt; \\epsilon$. Here, there is a ...

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)?

Nov 27, 2019 · Your answer is already solved, but I would like to add a trick. If the rank of an nxn matrix is smaller than n, the determinant will be zero.