factorial - Why does 0! = 1? - Mathematics Stack Exchange
The product of 0 and anything is $0$, and seems like it would be reasonable to assume that $0! = 0$. I'm perplexed as to why I have to account for this condition in my factorial function (Trying to learn …
combinatorics - Why is 0 factorial equal to 1? Is there any pure basic ...
Feb 6, 2021 · $$ 0! = \Gamma (1) = \int_0^ {\infty} e^ {-x} dx = 1 $$ If you are starting from the "usual" definition of the factorial, in my opinion it is best to take the statement $0! = 1$ as a part of the …
algebra precalculus - Zero to the zero power – is $0^0=1 ...
@Arturo: I heartily disagree with your first sentence. Here's why: There's the binomial theorem (which you find too weak), and there's power series and polynomials (see also Gadi's answer). For all this, …
Is $0$ a natural number? - Mathematics Stack Exchange
Inclusion of $0$ in the natural numbers is a definition for them that first occurred in the 19th century. The Peano Axioms for natural numbers take $0$ to be one though, so if you are working with these …
exponentiation - Why is $0^0$ also known as indeterminate ...
04 = 0 0 4 = 0 03 = 0 0 3 = 0 02 = 0 0 2 = 0 01 = 0 0 1 = 0 00 = 0 0 0 = 0 Right here, it seems like 00 0 0 can be equal to either 0 0 or 1 1 as proven here. This must be why 00 0 0 is indeterminate. Do you …
complex analysis - What is $0^ {i}$? - Mathematics Stack Exchange
Jan 12, 2015 · 0i = 0 0 i = 0 is a good choice, and maybe the only choice that makes concrete sense, since it follows the convention 0x = 0 0 x = 0. On the other hand, 0−1 = 0 0 1 = 0 is clearly false (well, …
definition - Why is $x^0 = 1$ except when $x = 0$? - Mathematics …
Jul 20, 2010 · If you take the more general case of lim x^y as x,y -> 0 then the result depends on exactly how x and y both -> 0. Defining 0^0 as lim x^x is an arbitrary choice. There are unavoidable …
Why does 0.00 have zero significant figures and why throw out the ...
Aug 10, 2023 · A value of "0" doesn't tell the reader that we actually do know that the value is < 0.1. Would we not want to report it as 0.00? And if so, why wouldn't we also say that it has 2 significant …
Why Not Define $0/0$ To Be $0$? - Mathematics Stack Exchange
Nov 8, 2013 · That $0$ is a multiple of any number by $0$ is already a flawless, perfectly satisfactory answer to why we do not define $0/0$ to be anything, so this question (which is eternally recurring it …
I have learned that 1/0 is infinity, why isn't it minus infinity?
@Swivel But 0 does equal -0. Even under IEEE-754. The only reason IEEE-754 makes a distinction between +0 and -0 at all is because of underflow, and for +/- ∞, overflow. The intention is if you have …