factorial - Why does 0! = 1? - Mathematics Stack Exchange
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 …
How can i construct a choice function for 1 or 2 arbitrary sets?
2 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, …
When 0 is multiplied with infinity, what is the result?
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 …
trigonometry - Why are angles in degrees converted into degrees ...
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 …
Who first defined truth as "adæquatio rei et intellectus"?
Mar 28, 2022 · António Manuel Martins claims (@44:41 of his lecture "Fonseca on Signs") that the origin of what is now called the correspondence theory of truth, Veritas est adæquatio rei et …
Grothendieck's existence theorem for affine algebras
5 days ago · Start asking to get answers Find the answer to your question by asking. Ask question
epistemology - Did Kant actually read Aristotle or did he just become ...
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 …
What are the criteria for "bad faith" questions?
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 …
Is it really impossible to use hexagons for mixed-resolution cover?
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 …
What is the difference between Fourier series and Fourier ...
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)?