A 'sum' is a sequence of terms joined by addition.
A 'product' is a sequence of terms joined by multiplication.
Is there a general term for terms joined by a general associative operation, that mathematicians would know? Is it 'sequence'?
In Haskell this would be implemented as a fold, but what do you call the thing it acts on? 'Iterable' and 'Enumerable' are too computer-sciencey.
It's possible this question has no good answer.
@christianp Induction/recursion principle maybe? Or σ-algebra.
@christianp Anyway, you can always speak about a sequence of elements in a magma…
@amiloradovsky yeah, I wanted to know: in something like `fold f x`, what kind of thing is x? The haskell wiki says "a data structure", which is far too broad. I'm thinking of an ordered set, so 'sequence' is the best I can come up with
@christianp Well, I could also imagine folding over trees, given by two binary operations — one for breadth and one for depth. There may be other generalizations.
@amiloradovsky yeah, I'm not interested in those generalisations for the thing I'm working on
@christianp P.S. The most general structure that may be folded with just a total binary operation is probably a well-ordered (sub)set.
A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.
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