In Axler's Linear Algebra Done Right,
Beside the proof of the Replacement Theorem: that is the length of the list of linearly independent vectors is less than or equal to the list of spanning vectors, there is a comment:
"Suppose that for each positive integer m, there exists a linearly independent list of m vectors in V . Then Replacement Theorem implies that V is infinite dimensional."
How does Replacement Theorem imply this?