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 …

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 …

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 …

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 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)?

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

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...

Jun 2, 2022 · To find the Laplacian at a point (x, y) (x, y) with y = 1 y = 1 you cannot put y = 1 y = 1 in the beginning and start differentiating. You have to first find uxx +uyy u x x + u y y at a general point …

Nov 25, 2011 · The following formula for $\\pi$ was discovered by Ramanujan: $$\\frac1{\\pi} = \\frac{2\\sqrt{2}}{9801} \\sum_{k=0}^\\infty \\frac{(4k)!(1103+26390k)}{(k!)^4 396^{4k ...

May 21, 2025 · A ver, por tu nombre supongo que hablas español, y además el ejemplo/ejercicio es de uno de los libros de Luis Rincón. Lo que propones si está correcto de forma didacta y para entender …