Abstract
- Concise, Polished Mathematical Argument explaining the validity of Mathematical Statement
- There are 2 types of proofs - Direct Proof and Indirect Proof (反证法)
Important
We can use Theorem (定理) to supporting the proof. A proof can be traced back to to Axioms (公理), along with accepted Rule of Inference (推理规则).
Concise
- There is no irrelevant details
Polished
- Should be the final drift
Without Loss Of Generality (WLOG)
- Used before an assumption in a proof which narrows the premise to some special case
- And implies that proof for that case can be easily applied to all other cases
- To remove very similar proof, for example,
a&bare two consecutive odd number. We need to proof the product of the 2 consecutive odd numbers is always odd - we need to proof it correct for both
a<b&b<acases, we can remove proof for one of the cases usingWLOG