>>13521597Terms in your logic. E.g. sets.
The first order theory of natural numbers, Peano arithmetic, has all the naturals as terms, but it doesn't have an object representing the natural numbers.
If a function from N to N is a collection of pairs and a mathematical object in itself, then it's an infinite set. E.g.
def f(n) := n^2 + 1
becomes the infinite set (data of a function graph)
f = {(0, 1), (1, 2), (2, 5), (3, 10), (4, 15), .... (k, k^2+1), ...}
If you want to make a proposition about f, e.g. that it's return values alternatve between odd and even, then to phrase this in the standard set theory sense you need this infinite collection as an object in itself.
