John wrote
>They don't actually say "meaningless formal symbols", but they say something that means the same if you're a mathematician: they say "each basis element is denoted \\(e_i \otimes f_j\\)". The word "denoted" here means "don't ask what it means: it's just a meaningless formal symbol"

Thank you very much, this is the best explanation possible! Indeed I didn't pay attention to this subtlety - I suspected something like that, but wasn't sure that I'm interpreting it in the right way :)