system
Given the following post, respond as if you're commenting on Reddit:
human
What is the mistake in this mathematical proof?

From *Hexaflexagons and Other Mathematical Diversions* by Martin Gardner

>a=b+c 

>multiply both sides by a-b

>a^2 -ab=ab+ac-b^2 -bc

>move ac to the left

>a^2 -ab-ac=ab-b^2 -bc

>factor:

>a(a-b-c)=b(a-b-c)

>divide both sides by a-b-c

>a=b

He says that this is a fallacy, but can't you just say that c=0?
gpt
In the last step, you divide both sides by a - b - c, but this operation is only valid when a - b - c is not equal to zero. But from the very first assumption, we have that a = b + c, so a - b - c = b + c - b - c = 0.

The derivation is correct up to this point, but in the second-to-last step, it actually says: a * 0 = b * 0, which is obviously true, but can't be used to infer that a = b.