What is Simple Deductive Proof?
Simple Deductive Proof: A method of demonstrating the truth of a mathematical statement through a sequence of logical, justified steps , each following necessarily from the previous one.
In mathematics, new knowledge can only be established through proof. Unlike science, where experiments test hypotheses, mathematics relies entirely on logical reasoning from previously accepted facts (axioms and theorems). This is what gives mathematics its certainty , and its beauty.
At SL level, proofs are focused on a specific, manageable task: showing that one side of an equation is equal to the other through valid algebraic manipulation. You are not expected to construct complex proofs from scratch, but you must be able to follow and present clear, logical arguments.
There are two main types of proof you will encounter at this level:
- Numerical proofs , verifying a relationship using specific numbers
- Algebraic proofs , establishing a general truth using variables
Algebraic proofs are more powerful than numerical ones. Checking that something works for and does not prove it works for all values of . A general algebraic argument is required for a complete proof.