Direct Proof

What is a direct proof?

A direct proof is a method of mathematical proof that establishes a statement's truth by showing that if we assume initial statements (hypotheses) to be true, then through logical steps, it leads directly to the conclusion we want to prove.

To demonstrate that P implies Q (P → Q) you show how you can get from P to Q through valid logical steps. Each step follows necessarily from the previous ones, creating a clear chain of reasoning from start to finish.

The beauty of a direct proof is its straightforwardness - you move forward step by step, using only valid logical operations, until you reach your goal.

Let's prove Pythagoras theorem with a direct proof!

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side, opposite to the right angle) equals the sum of squares of the other two sides.