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How to prove the following?

  1. Sep 15, 2008 #1
    Hey guys,

    do you now how to prove that the statement "there exists X such that for all Y and Z X+Y=Z" is FALSE. Seems easy but I can't figure out any counter example to the statement.

  2. jcsd
  3. Sep 15, 2008 #2


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    Science Advisor

    Do you understand WHY it is false? "There exists X such that for all Y and Z, X+ Y= Z" means that we can find a specific X such X+ Y= Z for any Y and Z- in other words, X is chosen FIRST. That is there must exist a specific number X so that X+ Y= Z for any Y and Z.

    X+Y= Z is the same as X= Z- Y. Okay, suppose X= -1. Choose Y= 2 and Z= 3. X+ Y= -1+ 2= 1 which is NOT equal to Z= 3. The statement is false for X= -1. Now suppose X is any number other than -1. Let Z= X+1 and Y= X+ 2. Then X+ Y= X+ X+ 2= 2X+ 2. That is equal to Z=X+ 1 only if 2X+2= X+ 1 or X= -1 which is false.
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