Question

How do proofs work?

Answer 1

What sort of proofs are you referring to? trigonometric, differential equations, advance calculus, real analysis...

Answer 2

The ones you do in geometry

Answer 3

I know it sounds kind of stupid! haha! I just don't get it

Answer 4

well, proofs are basically to show some form of mathematical statement is true.

Answer 5

assumed to be true*

Answer 6

Yep, agreed, there's a large gap between proofs done in Geometry than those in Linear Algebra.

So, we're taking some basic axioms, right? Things that cannot be broken down further, and then we take logical steps. When something implies something else, it means that, using the assumptions given, we receive the desired result. Continuing to do this yields lemmas and then, in end, a proof.

Answer 7

But sometimes the way how I proove it is short and simple when I see proof answers that are long and too detailed

Answer 8

Because you have to be extremely specific and careful to make sure that every single step you take is actually something that you've proved previously.