mutually commutative vs. pairwise commutative [mathematics]

udoh

Member
German - Germany
Hello,

In mathematical texts one often finds expressions like a_1, ... a_n are mutually commutative / pairwise commutative. This usually means that a_i a_j = a_j a_i for all i,j=1, ..., n. (Oft course, I assume here that these expressions have some mathematical meaning in some sense, i.e. that the products involved are defined.)

I would like to ask if there is a difference between these expressions. I know that the words mutually and pairwise have different meanings. But I do not see any mathematical difference here. Is one of them preferable? If so, why?

Best regards,
udoh
 
  • owlman5

    Senior Member
    English-US
    I prefer "mutually" although I'm no mathematician. The adverb "mutually" sounds more ordinary than does "pairwise".
     
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