LOGIC & PROOF

• Logic is the study of reasoning.

• Logic examines general forms which arguments may take, which forms are valid, and which are fallacies.

• Two parts of logic :

Inductive reasoning - give general conclusion from specific example.

Deductive reasoning - give logical conclusion from definitions and axioms.

• In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true.

• Also, proof is a sequence of inferences that starts with the axioms, and leads to the particular statement you wish to prove.

• A proof must demonstrate that a statement is true in all cases, without a single exception.

• Some terms :

Conjecture - An unproved that is believed to be true.

Theorem - The statement that is proved.

Lemma - The statement which use as a stepping stone in the proof of another theorem.