I can't seem to wrap my head around this proof of rational numbers and integers.
The statement says:
For all rational numbers a, there is a rational number b, such that a + b is not an integer.
I say this statement is true.
I would suppose there is a rational number a, where a = p/q for some integers p and q.
But I'm not sure what to let b equal, in order for it to be a rational every time. I've tried letting b equal some manipulation of a, but nothing seem to work. For example, I tried letting b = 1/a or q/p. But it p was 0, then b is undefined and wouldn't work.
Can I get help on this please?
Thanks in advance!