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what is the point of math proofs. To be perfectly rigorous the trivial steps should be either axioms or theorems proven in equally rigorous manner and references to said proofs. Proof using the Kakutani fixed-point theorem.
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In logic and mathematics a formal proof or derivation is a finite sequence of sentences each of which is an axiom an assumption or follows from the preceding sentences in the sequence by a rule of inference. MATHEMATICAL PROOFS DIRECT def. Being able to write down a valid proof may indicate that you have a thorough understanding of the problem.
Proofs are examples of exhaustive deductive reasoning which establish logical certainty to be distinguished f.
Being able to write down a valid proof may indicate that you have a thorough understanding of the problem. But there is more than this to it. In printed English language texts the formal statements of theorems lemmas and propositions are set in italics by tradition. An aesthetic term referring to the ability of an idea to provide insight into mathematics whether by unifying disparate fields introducing a new perspective on a single field or by providing a technique of proof which is either particularly simple or which captures the intuition or imagination as to why the result it proves is true.
