Dec 21, 2022 · Division is the inverse operation of multiplication, and subtraction is the inverse of addition. Because of that, multiplication and division are actually one step done together from left to …

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 …

HINT: You want that last expression to turn out to be $\big (1+2+\ldots+k+ (k+1)\big)^2$, so you want $ (k+1)^3$ to be equal to the difference $$\big (1+2+\ldots+k+ (k+1)\big)^2- (1+2+\ldots+k)^2\;.$$ …

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 …

Nov 29, 2013 · the Taylor series for ln (x) is relatively simple : 1/x , -1/x^2, 1/x^3, -1/x^4, and so on iirc. log (x) = ln (x)/ln (10) via the change-of-base rule, thus the Taylor series for log (x) is just the Taylor …

"Infinity times zero" or "zero times infinity" is a "battle of two giants". Zero is so small that it makes everyone vanish, but infinite is so huge that it makes everyone infinite after multiplication. In …

Oct 3, 2021 · Want to improve this question? As written, this question is lacking some of the information it needs to be answered. If the author adds details in comments, consider editing them into the …

Sep 6, 2011 · Does anyone have a recommendation for a book to use for the self study of real analysis? Several years ago when I completed about half a semester of Real Analysis I, the instructor used …

Apr 6, 2017 · (The general formula of Legendre Polynomial s is given by following equation: $$ P_k (x)=\sum_ {m=0}^ {\frac {k} {2}|\frac {k-1} {2}} {\frac { (-1)^m (2k-2m)!} {2^km ...

Feb 23, 2018 · Are you're probably aware, there are common special notations for inverses of certain special functions, e.g., $\arctan$, $\operatorname {arsinh}$, etc. (Of course, $\arctan$ is not the …