No they don't.
Primary schools say that sort of thing. If you do proofs of the density of the rationals and other such proofs it talks about
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. For all the proofs it doesn't have lemmas, or WLOG, or ICBST every time saying and now you do it for the integers.
Most of my maths textbooks on algebra and calculus say what
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means.
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Most maths books use quotient groups for the sort of malarkey you're talking about.