How would you know that 0.005 is not excluded from the value 0? In the context of natural numbers and finite combinatorics it is generally safe to adopt a convention that $0^0=1$. The product of 0 and anything is $0$, and seems like it would be reasonable to assume that $0!
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Extending this to a complex arithmetic context is fraught with risks, as is. Defining 0^0 as lim x^x is an arbitrary choice. 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.
I heartily disagree with your first sentence.
It is perfectly reasonable to. Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly $0$ was considered i. Show that ∇· (∇ x f) = 0 for any vector field [duplicate] ask question asked 9 years, 9 months ago modified 9 years, 9 months ago
For example, $3^0$ equals 3/3, which equals $1$, but $0^0$ equals 0/0, which equals any number, which is why it's indeterminate. In fact how would you know that any value is excluded? The uncertainty might be extremely high. = 1$ as a part of the.
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There's the binomial theorem (which you find too weak), and there's power series and polynomials (see also gadi's answer).
I'm perplexed as to why i have to account for this condition in my factorial function (trying to learn. Also, 0/0 is undefined because of what i just said.
