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Regardless of the wording being exact or not, ChatGPT’s answer is incorrect in its contents. The statement “exactly one” requires the parallel postulate, since
by layer8 2y ago
Regardless of the wording being exact or not, ChatGPT’s answer is incorrect in its contents. The statement “exactly one” requires the parallel postulate, since otherwise it’s not necessarily true. Specifically in spherical geometry, which is considered to be consistent with Euclid’s first four postulates (i.e. without the parallel postulate).
The bottom line is, you can’t take any single LLM statement at face value, even in seemingly easy to answer cases like this.
- roywiggins 2y agoit's the point-line postulate, you can use it as part of a set of axioms equivalent to Euclid but it definitely not one of Euclid's https://en.wikipedia.org/wiki/Point%E2%80%93line%E2%80%93plane_postulate https://en.wikipedia.org/wiki/Point%E2%80%93line%E2%80%93pla...