A

**geometric proof**involves writing reasoned, logical explanations that use definitions, axioms, postulates, and previously proved theorems to arrive at a conclusion about a**geometric**statement.In this way, what is the definition of formal proof?

A

**formal proof**or derivation is a finite sequence of sentences (called well-formed formulas in the case of a**formal**language) each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference. The last sentence in the sequence is a theorem of a**formal**system.Why is proof in mathematics important?

All mathematicians in the study considered

**proofs**valuable for students because they offer students new methods,**important**concepts and exercise in logical reasoning needed in problem solving. The study shows that some mathematicians consider proving and problem solving almost as the same kind of activities.What is the mathematical definition of a proof?

In

**mathematics**, a**proof**is a deductive argument for a**mathematical**statement. In the argument, other previously established statements, such as theorems,**can**be used. In principle, a**proof can**be traced back to self-evident or assumed statements, known as axioms, along with accepted rules of inference.