Single Idea 17762

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry]

Full Idea

Since non-Euclidean geometry preserves all Euclid's postulates except the fifth one, all the theorems derived without the use of the fifth postulate remain valid.

Gist of Idea

In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate


Michal Walicki (Introduction to Mathematical Logic [2012], 4.1)

Book Reference

Walicki,Michal: 'Introduction to Mathematical Logic' [World Scientific 2012], p.122