What is a Proof?
- In mathematics, you cannot just make claims, you'll need some sort of proof to do so.
- All mathematical formulas have some sort of proof to show that they do actually work.
- A proof in mathematics often consists of a logical set of steps that validates the truth of a general statement beyond any doubt.
- There are various ways to prove something in mathematics.
- Direct proof, proof by contradiction and proof by induction are the most commonly used.
Direct Proof
- A direct proof is a way of showing the truth of a given statement by constructing a series of reasoned connected established facts.
- These facts can be proven mathematical laws or formulae, for example.
- In a direct proof the following steps are used:
Identify the given statement
Use axioms, theorems, etc. to make deductions that prove the conclusion of your statement to be true.
Example
Sources