Infinite Rays in Trees

Question

I was wondering if it was possible to have an infinite ray in a finite tree? This is impossible merely from the fact that an infinite ray goes through infinite vertices, contradicting the finiteness of the tree right?

Is it fine if I just stated this as an obvious lemma?

Thanks.

Answer 1

That a finite tree cannot contain an infinite path doesn’t even rate as a lemma. It is at most a passing remark that follows immediately from the definitions of finite, infinite, tree, and path.