1=0 !!!!!

The following is a "proof" that one equals zero.

Consider two non-zero numbers x and y such that

x = y.
Then x² = xy.
Subtract the same thing from both sides:
x² - y² = xy - y².
Dividing by (x-y), obtain
x + y = y.
Since x = y, we see that
2 y = y.
Thus 2 = 1, since we started with y nonzero.
Subtracting 1 from both sides,
1 = 0.

What's wrong with this "proof"?

The Math Behind the Fact:
The problem with this "proof" is that if x=y, then x-y=0. Notice that halfway through our "proof" we divided by (x-y).

Remember : This is a reminder for students to always check when they are dividing by unknown variables for cases where the denominator might be zero.