4 ms·
No, they're saying that what is true in mathematics is contingent, not absolute. It all depends on which set of axioms use, what assumptions you make. The area
by chongli 2mo ago
No, they're saying that what is true in mathematics is contingent, not absolute. It all depends on which set of axioms use, what assumptions you make.
The area of a triangle doesn't have 1 unique formula, it has many, depending on the system you use. A triangle in plane geometry has a different area than a triangle in spherical geometry, and different again in hyperbolic geometry.
When you get to studying the geometry of manifolds, you realize the area of a triangle can be any damn thing you want, depending on how you construct the manifold you embed it in.
- cman1444 2mo agoThis is a needless qualifier for the argument at hand. A proof can just be "assuming these axioms.....the area of a triangle is X"