## 101Ryan101 Group Title Medals for ones who prove: 0^0 = 1 (I wrote the last one wrong) :/ 3 years ago 3 years ago

1. angela210793

every no in exponent 0 is =1.....idk how to prove tht though :(...my teacher has never asked me tht and she has never proved tht to me O.o...sorry :/

2. ragnarok23

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.

3. 101Ryan101

Is there an algebraic proof involving an equation?

4. 101Ryan101

It seems more intuitive that the answer would be 0 to me, that's all.

5. joemath314159

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: $(x-x)^0 = \left(\begin{matrix}0 \\ 0\end{matrix}\right)x^0(-x)^0 \iff 0^0 = 1$

6. jimmyrep

3^8 / 3^8 = 1 = 3^(8-8) = 3^0

7. 101Ryan101

Thanks Joe, I don't understand that proof but it helps to know that it's beyond my level at this point.

8. joemath314159

>.< 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.

9. 101Ryan101

no, it's fine.. I'm serious.. thax... Just wanted to look into this and get some feedback is all..

10. 101Ryan101

Jimmyrep! nice! that's a good one for me to grasp..