@christianp I'd probably argue that "product" has a more general meaning in mathematics, even at school level (A level anyway). https://en.wikipedia.org/wiki/Product_(mathematics)#Products_in_linear_algebra
More abstractly, associativity holds for semigroups and people talk about products there, too.
@pkra yeah, that's unfortunate, because it's such an overloaded term. If I say 'products', then a large portion of my readers will assume it doesn't include sums
@christianp also, I vaguely recall from getting my maths A level that "doing sums" was often used generically for "solve the problem" in the UK. Arguably, a long long time ago...
@pkra I didn't know you had maths A level!
Yes, 'doing sums' is often used to mean any calculation.
@christianp indeed, I do. Good to know that my British English is not completely out of date (yet).
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