Do you not care if your vector space has a basis?
It is nicer to state theorems that hold for all vector spaces, so mathematicians like to invoke AoC. However, in any applications that are practically relevant, you can obtain a basis without invoking AoC.
It is nicer to state theorems that hold for all vector spaces, so mathematicians like to invoke AoC. However, in any applications that are practically relevant, you can obtain a basis without invoking AoC.