# Ge - ne - ral - lize - za - tion - s

Level pending

It seems like I have proven that for $$\forall \ x \in \mathbb R$$ and $$\forall \ y \in \mathbb N^*$$; $$x^y = 1$$

Here's the prove:

Step 1: We have that $$x^0 = 1$$.

Step 2: Assume that $$x^k = 1; \forall \ 0 \le k \le y$$.

Step 3: We have that: $x^{y + 1} = \dfrac{x^y \cdot x^y}{x^{y - 1}} = 1$ This is true for $$k = y + 1$$.

Step 4: Using inductive reasoning, the statement above is true for $$\forall \ y \in \mathbb N^*$$.

I sent this prove to my teacher, and she said I was wrong at some point.

Where did I go wrong in this prove?

(This is actually a real story a while ago.)

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