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## Main Question or Discussion Point

This is not a hw question, just a question that popped into my head over the weekend.

My apologies if this is silly, but would you say that the symmetric group S4 is a subset of S5? My friends and I are having a debate about this. One argument by analogy is that we consider the set of reals to be a subset of the complex numbers (R2 with multiplication defined in some fashion, right?), where the reals are of the form (a,0) for a a real number, and so we should also be able to think of S4 as a subset of S5.

My apologies if this is silly, but would you say that the symmetric group S4 is a subset of S5? My friends and I are having a debate about this. One argument by analogy is that we consider the set of reals to be a subset of the complex numbers (R2 with multiplication defined in some fashion, right?), where the reals are of the form (a,0) for a a real number, and so we should also be able to think of S4 as a subset of S5.