01 · AXIOMS vs POSTULATES
What are Axioms and Postulates?
• Axioms: Basic truths assumed without proof used throughout mathematics.
• Postulates: Assumptions specific to geometry.
EUCLID'S 7 AXIOMS
Euclid's Common Notions
1. Things which are equal to the same thing are equal to one another (If A = B and B = C ⟹ A = C).
2. If equals are added to equals, the wholes are equal.
3. If equals are subtracted from equals, the remainders are equal.
4. Things which coincide with one another are equal to one another.
5. The whole is greater than the part (If A = B + C where C > 0 ⟹ A > B).
6. Things which are double of the same things are equal to one another.
7. Things which are halves of the same things are equal to one another.