Let $\{e_i\}_{i\in I}$ be a basis for V where $I$ is some totally ordered indexing set. Fix $k\in \mathbb{Z}^{\geq 0}$. Do we get an induced basis on $\bigwedge^k V$, where $$\{e_1\wedge...\wedge e_k|e_i\in \{e_i\}\}$$ where we use the ordering on $I$ to order lowest to highest from left to right.


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