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Math Help - Disprove proof of 2=1

  1. #1
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    Disprove proof of 2=1

    Here is what the teacher has given us:

    a=b for some a, some b
    a+a=a+b (add a to both sides)
    2a=a+b
    2a-2b=a+b-2b (subtract 2b from oth sides)
    2(a-b)=a+b-2b [2a-2b=2(a-b)]
    2(a-b)=a-b
    2+ 1 (divide by a-b)

    One step here is wrong, or so the teacher says. Which one is it?
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  2. #2
    MHF Contributor
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    a=b for some a, some b
    a+a=a+b (add a to both sides)
    2a=a+b
    2a-2b=a+b-2b (subtract 2b from oth sides)
    2(a-b)=a+b-2b [2a-2b=2(a-b)]
    2(a-b)=a-b
    2 = 1 (divide by a-b)

    One step here is wrong, or so the teacher says. Which one is it?
    The last step, the division by (a-b).

    You said a=b at the beginning. If that is so, then a-b = 0.
    Hence, since you cannot divide by zero, then the last step is wrong.
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  3. #3
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    Wow, thanks, that's absolutely right! I can't believe I overlooked that. Thanks!
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