I was in the middle of proving something when I reached a contradiction, that .5 + an integer = an integer. However, this cannot be true, and I'm curious if its acceptable to just say that by definition of integers .5 + an integer is not an integer, or do I have to prove it?(adsbygoogle = window.adsbygoogle || []).push({});

Furthermore, if I have to prove it, how would I go about this? I would say let x and y be integers, so x + .5 = y, right?

Since x and y are integers then x = x/1 and y = y/1, so x/1 + 1/2 = y/1.

2x/2 + 1/2 = y/1

so

(2x + 1/2)/2 = y/1

and then... If I said that 2x +1/2 was not a whole number so dividing it by two must give a fraction, and thus it can't be reduced to a whole number over 1... That doesn't sound like it works though becuase its just restating what I was trying to prove... Not to mention I'm not sure I can even say that a fraction divided by two doesn't give a whole number... Any ideas? Thanks.

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# Homework Help: Proof Question: Prove integer + 1/2 is not an integer

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