Idle thought: with the exception of $$\sum$$ and $$\prod$$, transforming an associative binary operation into an agglomerative "summation notation" is just making the symbol big and adding sub/superscripts. E.g., $$\bigotimes_{i=0}^n v_i$$. It's strange to me that this applies to non-commutative operators ( $$\wedge$$ ), but also that there are many binary operations where this rule can't be applied due to limitations of the syntax (bracket operators, function composition, modulo).

Like, doing this just feels weird: $$\bigcirc_{i=1}^nf_i := f_1 \circ f_2 \circ \dots \circ f_n$$

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