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 …
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 …
$\\forall x \\in \\mathbb{R}, f'(x) > f(f(x))$, Prove that for all $x ...
Jan 5, 2026 · I was thinking of using the property which we derive, f is monotnoic so f (f (x) will be monotnically inreasing. Now that being said, above condition doesnt qualify for this property which is …
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 …
moral dilemma - The Trolley’s Sixth Victim and the Invisible Killer ...
Jan 21, 2026 · I have been thinking about the classic Trolley Problem, and I see two major issues that are rarely discussed. The Operator is the Sixth Victim (Moral Injury) I see the lever operator not as …
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 does it mean to have a determinant equal to zero?
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.
Is this Ethical Sentience proposal good? - Philosophy Stack Exchange
Feb 9, 2026 · My proposal on Ethical Sentience: "I believe a Respected Entity is any independently responsive being, capable of both pleasure and pain, whose will arises from self …
Is there a logical fallacy for confusing means with ends?
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 …
What did John Austin (died 1859) mean by habit, habitual(ly)?
Jan 21, 2026 · I reiterate the only sensible suggestion: to read the text. The source is John Austin (legal philosopher: 1790 - 1859) 's treatise The province of jurisprudence determined (1832), page 199 of …