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 axioms (and a lot of natural number theory does) then you take $0$ to be a natural number.
definition - Why is $x^0 = 1$ except when $x = 0$? - Mathematics Stack ...
1) x^a × x^b = x^a+b; for x = 0 and a = 0, you would get 0^0 × 0^b = 0^b = 0, so we can't tell anything -- except confirm that 0^0 = 1 still works here! 2) x^{-a}=1/{x^a} -- so when a = 0 , x^{-0} = 1/x^0 = x^0 , which again does work for 0^0 = 1 ; 3) {x^a}^b = x^{a×b} , thus x^(1/n) is the n-th root -- and 1/n = 0 for no value of n , so ...
Zero power zero and $L^0$ norm - Mathematics Stack Exchange
$\begingroup$ This definition of the "0-norm" isn't very useful because (1) it doesn't satisfy the properties of a norm and (2) $0^{0}$ is conventionally defined to be 1. $\endgroup$ – Brian Borchers
Show that ∇· (∇ x F) = 0 for any vector field [duplicate]
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Show that $L^p$ "space" for $0
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limit when zero divided by infinity - Mathematics Stack Exchange
On the contrary, those limits tell you that the limit of the entire quotient is $0$. This may be easier to see if you rewrite to $$ \lim_{x\to\infty} f(x)\frac1{h(x)} $$ where $\lim_{x\to\infty} f(x) = 0 $ and $\lim_{x\to\infty} \frac1{h(x)}=0 $, and the product of two functions that both have limit $0$ surely also has limit $0$.
Finding the limit when denominator = 0 - Mathematics Stack Exchange
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Limit of $\\frac{x^c-c^x}{x^x-c^c}$ as $x \\rightarrow c$
My question is: Show that $\lim_{x \rightarrow c} \frac{x^c-c^x}{x^x-c^c}$ exists and find its value. Because the limit is 0/0 I've tried using L'Hopital's rule, but every time I differentiate it I
limits - Prove that $\lim \limits_{n \to \infty} \frac{x^n}{n!} = 0 ...
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