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17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
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. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 4.1) |
17754 | Inductive proof depends on the choice of the ordering [Walicki] |
Full Idea: Inductive proof is not guaranteed to work in all cases and, particularly, it depends heavily on the choice of the ordering. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.1.1) | |
A reaction: There has to be an well-founded ordering for inductive proofs to be possible. |