A Vector Space is Infinite-Dimensional iff there exists an Infinite Linearly Independent Set

Last updated Nov 1, 2022

Let $V$ be a Vector Space. Then $V$ is an Infinite-Dimensional Vector Space If and Only If there exists Linearly Independent $R \subset V$ so that $|R| = \infty$.

Follows from A Vector Space is Infinite-Dimensional iff its Linearly Independent Set Size is Unbounded and Linearly Independent Set Size is Unbounded iff there exists an Infinite Linearly Independent Set. $\blacksquare$