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Medals for ones who prove: 0^0 = 1 (I wrote the last one wrong) :/

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every no in exponent 0 is =1.....idk how to prove tht though :( teacher has never asked me tht and she has never proved tht to me O.o...sorry :/
There's a combinatorial argument. Consider trying to arrange 0 objects in a line - this is 0^0. There's exactly one way to do this: do nothing.
Is there an algebraic proof involving an equation?

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It seems more intuitive that the answer would be 0 to me, that's all.
you could use the binomial theorem, and the fact that 0! = 1 \[(x+y)^n = \left(\begin{matrix}n \\ 0\end{matrix}\right)x^n+\left(\begin{matrix}n \\ 1\end{matrix}\right)x^{n-1}y+\ldots+\left(\begin{matrix}n \\ n\end{matrix}\right)y^n\] \[=\sum_{i=0}^{n}\left(\begin{matrix}n \\ i\end{matrix}\right)x^{n-i}y^i\] Let n = 0, and y = -x, we end up with: \[(x-x)^0 = \left(\begin{matrix}0 \\ 0\end{matrix}\right)x^0(-x)^0 \iff 0^0 = 1\]
3^8 / 3^8 = 1 = 3^(8-8) = 3^0
Thanks Joe, I don't understand that proof but it helps to know that it's beyond my level at this point.
>.< im sry, is there a certain part of it you dont understand? i only have 15 mins till my next class, but im down to try and explain.
no, it's fine.. I'm serious.. thax... Just wanted to look into this and get some feedback is all..
Jimmyrep! nice! that's a good one for me to grasp..

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