Find a set A (subset of R,set of real numbers) and an element a of R

[julia89]

Find a set A (subset of R,set of real numbers) and an element a of R
such that there is no bijecton from a+A(we add a to the set A)to A.

I can't find a good example. Can someone help
Are we done if we choose the empty set? (And is the empty set a subset of R?)

Thank you

 

[HallsofIvy]

?? Any finite set will do. Take A= {1, 2, 3} and a= 0. Then A has 3 members while A+ a has 4. There cannot be a bijection from one to the other.

Yes, the empty set is a subset of R (it is a subset of any set). Choosing A= {} and a any real number so that A+ a= {a} will also work.