Possible Duplicate: Prove 0! = 1 0! = 1 from first principles Why does 0! = 1 0! = 1? All I know of factorial is that x! x! is equal to the product of all the numbers that come before it. The product …

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 …

"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 …

Dec 21, 2022 · You shouldn't think of either rule as setting different priorities for multiplication and division, or for addition and subtraction. You need to work left to right for these. PEMDAS = …

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 …

It might be helpful if you first introduce a new symbol to refer to one of the vector cross-products as a whole. E.g., let's define (a × b) =: x (a × b) =: x. Using the cyclic property of the scalar …

Apr 6, 2017 · I am trying to prove that 1 n! 2n dn dxn{(x2 − 1)n} =Pn(x) 1 n! 2 n d n d x n {(x 2 1) n} = P n (x), where Pn(x) P n (x) is the Legendre Polynomial of order n. I've been told that the …

The usual matrix multiplication is only defined for multiplying an m × n m × n matrix with an n × R n × R matrix. So the number of columns of the first matrix must be equal to the number of rows …

In 1910, Srinivasa Ramanujan found several rapidly converging infinite series of $\\pi$, such as $$ \\frac{1}{\\pi} = \\frac{2\\sqrt{2}}{9801} \\sum^\\infty_{k=0 ...

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, $\arctan$ …