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Math Help - Proving |a+b| = |a|+|b|

  1. #1
    Member rowe's Avatar
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    Proving |a+b| = |a|+|b|

    Hi guys, I'm doing a case by case proof of

    |a+b| \leq |a|+|b|

    from Spivak, and he says:

    When a \geq 0 and b \leq 0, we must prove that:

    |a+b| \leq a-b

    I'm a bit stuck on his line of reasoning, could someone explain why we have to prove the above?
    Last edited by rowe; June 5th 2010 at 06:28 AM.
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  2. #2
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    Quote Originally Posted by rowe View Post
    I'm doing a case by case proof of
    |a+b| = |a|+|b| from Spivak, and he says
    You cannot prove |a+b|=|a|+|b| because it is not true.
    So exactly what is the correct statement of this problem?
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  3. #3
    Member rowe's Avatar
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    Typo, sorry. Fixed original post
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  4. #4
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    Quote Originally Posted by rowe View Post
    Hi guys, I'm doing a case by case proof of

    |a+b| \leq |a|+|b|

    from Spivak, and he says:

    When a \geq 0 and b \leq 0, we must prove that:

    |a+b| \leq a-b

    I'm a bit stuck on his line of reasoning, could someone explain why we have to prove the above?
    Hi

    If a \geq 0 then |a| = a
    and if b \leq 0 then |b| = -b

    Therefore when a \geq 0 and b \leq 0, |a|+|b| = a-b
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