What is the diference between constructive proofs and formalist proofs?

Question

Exemples would be helpful.
Exemples of the same theorem demonstrated by the constructive and formalist way would be very nice.

Answer 1

constructive proof is when you construct an object with the desired properties, it is almost like an algorithm,
a formalist proof is just an argument that establishes the existance, but it does not help to find one concrete example..

example: formalistic proof:
the inverse funcion theorem, tells you that you can find an inverse in a small enough neiborhood of a point where the function es increasing (or decresing), but it does not provide a formula.

constructive proof:
if you have a regular curve, then there exist a unit-speed reparametrization. In this case the proof actually tells you that the inverse of the arc-length function is the desired parametrization

Answer 2

Off the top of my head I could not give you a specific example but, from what I recall, a constructivist proof would prove a proposition directly by devising a concrete mathematical entity; a formalist approach would rely on schemes such as proof by contradiction...sidestepping completely the need to actually construct a compelling scenario that would accomplish the same purpose.

Answer 3

Give it a day.. let's see what conversion takes place tomorrow. I wouldn't want you to have to spend all that money erecting a fence until you pick one and stick with it. The next religion might require NO fences.