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, $0^0=1$ is extremely convenient, and I wouldn't know how to do without it In my lectures, I always tell my students that whatever their teachers said in school about $0^0$ being undefined, we
Seeking elegant proof why 0 divided by 0 does not equal 1 The reason $0 0$ is undefined is that it is impossible to define it to be equal to any real number while obeying the familiar algebraic properties of the reals It is perfectly reasonable to contemplate particular vales for $0 0$ and obtain a contradiction This is how we know it is impossible to define it in any reasonable way
Why Not Define $0 0$ To Be $0$? - Mathematics Stack Exchange 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 seems) is superfluous
Equivalence of 0 and 0. 0 - Mathematics Stack Exchange 3 In ordinary mathematics, all representations of 0 are equivalent: $0=0 0=+0=-0$ and so on In computer programming, however, 0 may be different from 0 0, in that the former is an integer while the latter is a decimal (which may be floating-point or arbitrary precision)
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
Is zero odd or even? - Mathematics Stack Exchange Some books say that even numbers start from $2$ but if you consider the number line concept, I think zero($0$) should be even because it is in between $-1$ and $+1$ (i e in between two odd numbers)
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