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 …

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 …

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 …

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 …

Q&A for people studying math at any level and professionals in related fields

Apr 4, 2026 · Your numerical observations are correct and align precisely with the heuristic framework derived from Artin’s primitive root conjecture for algebraic numbers, combined with Chebotarev …

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.

Nov 24, 2024 · I have no idea how to approach the following homework problem. Prove the identity $$a^ {\log_b c} \equiv c^ {\log_b a}.$$

Mar 30, 2026 · Frazer Jarvis, Algebraic Number Theory, Lemma 6.22 ( Expression of an ideal in the ring of integers of the imaginary quadratic field )