1. If $W$ is a subspace of a vector space $V$ over a field $k$, then
$\dim_k W\leq\dim_kV$.
2. Sometimes you may hear people ask “what is the fourth dimension?” To you, the informed reader, this now appears to be an uninformed question. What they are trying to ask is “what does the 4-dimensional vector space $\mathbb R^4$ look like, and what is its fourth basis vector?” The first part of the question makes sense, but is hard to answer. The second part doesn’t make sense. Bases are just sets and therefore aren’t ordered. I could make “the fourth basis vector” whichever I want. If you ever get this question, just point somewhere and say “that way.” You can’t be wrong.