...union" of all single-point mappings. That's pretty trivial, and such a scheme will work for every construct that's binding a variable. And it's quite different from what happens with (finite) sums, products, and lattice operations. These are all non-trivial folds. If I'm inventive enough, I can of course find some binary operation everywhere. For example, every natural number is connected to the binary operation (+), because I can e...

...summation and integral are iterative forms of binary plus. 2. Pi-capital product is iterative form of multiplication. 3. Lattice supremum is iterative form binary meet. 5. Lattice infinum is iterative form binary join. 6. Existential and universal quatifiers are lattice supremum and infinum. Now, there must be a binary operation that lambda is iterative form as well? I agree....

... if you don't see them as a means of calculating truth values (in which case they reduce to lattice operations), but instead as elements of a formal language of mathematics, they become different from the other big ... way to express the limit with a binary operation. Just because this process works for four examples (sum, product, lattice operations) doesn't mean it has to work for all the other examples. You're trying to overgeneralize, ...

...summation and integral are iterative forms of binary plus. 2. Pi-capital product is iterative form of multiplication. 3. Lattice supremum is iterative form binary meet. 5. Lattice infinum is iterative form binary join. 6. Existential and universal quatifiers are lattice supremum and infinum. Now, there must be a binary operation that lambda is iterative form as well? This might...

...summation and integral are iterative forms of binary plus. 2. Pi-capital product is iterative form of multiplication. 3. Lattice supremum is iterative form binary meet. 5. Lattice infinum is iterative form binary join. 6. Existential and universal quatifiers are lattice supremum and infinum. Dirk Thierbach has already pinted out that this is only true when you iterate over finite sets....

...Pi-capital product is iterative form of multiplication. 3. Lattice supremum is iterative form binary meet. ...> 6. Existential and universal quatifiers are lattice supremum and infinum. Now, there must be a ... Same for "capital-pi" product. 3) Same for lattice supremum and infimum over finite sets. ... to see discussions i have had on orthomodular lattices and quantum logic or denotational and operational semantics ...

...? :-) 2. Pi-capital product is iterative form of multiplication. 3. Lattice supremum is iterative form binary meet. 5. Lattice infinum is iterative form binary join. 6. Existential and universal quatifiers are lattice supremum and infinum. Now, there must be a binary operation that lambda is... folds it. 2) Same for "capital-pi" product. 3) Same for lattice supremum and infimum over finite sets. In the case where X is ...

... and integral are iterative forms of binary plus. 2. Pi-capital product is iterative form of multiplication. 3. Lattice supremum is iterative form binary meet. 5. Lattice infinum is iterative form binary join. 6. Existential and universal quatifiers are lattice supremum and infinum. Now, there must be a binary operation that lambda is iterative form as well? ...

... summation and integral are iterative forms of binary plus. 2. Pi-capital product is iterative form of multiplication. 3. Lattice supremum is iterative form binary meet. 5. Lattice infinum is iterative form binary join. 6. Existential and universal quatifiers are lattice supremum and infinum. Now, there must be a binary operation that lambda is iterative form as well? ...

... summation and integral are iterative forms of binary plus. 2. Pi-capital product is iterative form of multiplication. 3. Lattice supremum is iterative form binary meet. 5. Lattice infinum is iterative form binary join. 6. Existential and universal quatifiers are lattice supremum and infinum. Now, there must be a binary operation that lambda is iterative form as well? if i ...