- Sigma summation is iterative form of binary plus.
- Pi-capital product is iterative form of multiplication.
- Lattice supremum is iterative form binary meet.
- Lattice infinum is iterative form binary join.
- Existential and universal quatifiers are lattice supremum and infinum.
- Integral is summation "in the limit".
Does any quantifier have associated binary operation; for example what generalized quantifiers like "more than 5" corresponds to? Positive answer to this question would hint to binary operation corresponding to the limit quantifier -- essentially we are looking into where sequence "majority" leads to.
Likewise, what might be a binary operation corresponding to lambda abstraction? Having associated binary operation greatly facilitates intuition behind quantifier; it can be thought of as just repetitive application of binary operation.