Prove: If D is a Dedekind Infinite set then D-{a} is Dedekind infinite.

Well, I can't figure out how to prove this. Just give me hints please :)

"Prove: If D is a Dedekind Infinite set then D-{a} is Dedekind infinite."

Intuitively, a is an element of D is also an assumption. Our Class Reference is the book "Introduction to Advanced Mathematics" by Barnier and Feldman

Please give me **only hints** on how to prove this :)

Re: Prove: If D is a Dedekind Infinite set then D-{a} is Dedekind infinite.

One does not need to assume that a ∈ D. If a ∉ D, then D - {a} = D, so it is still Dedekind-infinite.

Let f : D -> E be a one-to-one correspondence where E is a proper subset of D. Remove f(a) from E.