I know that if you have x-2, that's the same thing as saying 1/x2. But I'm just wondering what is the mathematical reasoning for why that's true?
I looked around a bit.I know that if you have x-2, that's the same thing as saying 1/x2. But I'm just wondering what is the mathematical reasoning for why that's true?
[/quote]1 is not considered a prime because allowing units would ruin the unique factorization theorem.
It's still rather vacuous. How many ways are there to spell a word with no letters? The answer is "1" if you're a mathematician and "what?" if you're not.There is reason for [tex]0^0 = 1[/tex] that it's more than just a definition. This is a particular (and extreme) case of a combinatorial equality.
I guess that's the more traditional way of looking at it, but I think the continuity result is simpler. You're treating exponentiation as a regular real-valued function on R^2 instead of a shorthand for some awkward limit.In the context of Analysis, [tex]0^0[/tex] is considered undefined because it stand for a shorthand for a limit of the form:
.... It doesn't have directly to do with the continuity [tex]x^y[/tex].