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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 Haskell).
Jan 12, 2015 · It is possible to interpret such expressions in many ways that can make sense. The question is, what properties do we want such an interpretation to have? $0^i = 0$ is a good choice, and maybe the only ...
Oct 9, 2013 · Is a constant raised to the power of infinity indeterminate? I am just curious. Say, for instance, is $0^\\infty$ indeterminate? Or is it only 1 raised to the infinity that is?
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 ...
@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 ex...
93 The other comments are correct: 1 0 1 0 is undefined. Similarly, the limit of 1 x 1 x as x x approaches 0 0 is also undefined. However, if you take the limit of 1 x 1 x as x x approaches zero from the left or from ...
Oct 28, 2019 · In the context of limits, $0/0$ is an indeterminate form (limit could be anything) while $1/0$ is not (limit either doesn't exist or is $\pm\infty$). This is a pretty reasonable way to think about why i...
Show that ∇· (∇ x F) = 0 for any vector field [duplicate] Ask Question Asked 9 years, 6 months ago Modified 9 years, 6 months ago
Jan 22, 2017 · For example, 0x = 0 0 x = 0 and x0 = 1 x 0 = 1 for all positive x x, and 00 0 0 can't be consistent with both of these. Another way to see that 00 0 0 can't have a reasonable definition is to look at th...
Feb 4, 2018 · So there is a sense in which the only "really geometrically meaningful" integral of $0$ is $0$ itself. But your friend is still wrong, since the term "integral" in this context means antiderivative and n...
