back to ideas for this text


Single Idea 17762

[from 'Introduction to Mathematical Logic' by Michal Walicki, in 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

Source

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

Book Reference

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