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.
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
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.