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 …

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 …

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 …

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 …

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 …

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 …

Dec 29, 2024 · Q&A for people studying math at any level and professionals in related fields

Hint: prove inductively that a product is $> 1$ if each factor is $>1$. Apply that to the product $$\frac {n!} {2^n}\: =\: \frac {4!} {2^4} \frac {5}2 \frac {6}2 \frac {7}2\: \cdots\:\frac {n}2$$ This is …

Nietzsche recalls the story that Socrates says that 'he has been a long time sick', meaning that life itself is a sickness; Nietszche accuses him of being a sick man, a man against the instincts of...

5 days ago · I want to show that the relation ≤ is transitive using axioms A1-A3. To show that we can introduce a natural partial order on the H- algebra