Hi,

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!