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    • Theorem One

    In which I showed that 1 was equal to 2. Which it isn't. Could you find the mistake in my "proof"?

    If a=b then a-b=0. Let's look at the critical lines of the proof again:

    a²-ab=(a-b)(a+b)
    a(a-b)=(a-b)(a+b)
    a=a+b
    a=a+a
    a=2a
    1=2

    Can you see the problem now?

    Let me narrow it down a little further:

    a(a-b)=(a-b)(a+b)
    a=a+b

    Remember, a-b=0. In the step between these two lines I am dividing by zero, which is not a well-defined mathematical operation.

    The proof is invalid.