While we can prove both De Morgan's terms, they are called "law/rule" in many textbooks, references and also Wikipedia(+)! why law?
Aren't those terms theorem, in fact?
Asked
Active
Viewed 491 times
5
-
DeMorgan was the great-great-...-great grandfather of Dredd. And as we all know, Dredd is THE LAW. – Asaf Karagila Feb 11 '14 at 16:52
-
Some older theorems where rather seen as absolute truths, specially those in the heart of logic. De Morgan's Laws are an example. – Pedro Feb 11 '14 at 18:52
2 Answers
5
The truth is that many results have non-standard names, like the ones you mention, the division algorithm, and Bertrand's postulate (which was not proved by Betrand). Then there are conjectures that will probably carry their names forevermore even after being proven (like Riemann's hypothesis); conjectures that were called "theorem" (like Fermat's last theorem, last because it was one of the few unproven results by Fermat that Euler wasn't able to prove, and withstood centuries of work). The strict theorem/lemma/corollary division is just fiction, there are people who prefer to call everything "proposition," there are plenty of lemmata which turned out much more important than the (now almost forgotten) results they led to. Mathemathics is a human endeavor, with plenty of quirks and vagaries.
vonbrand
- 27,812
3
The answer here is really helpful: Difference between a theorem and a law. I believe you are right though!
From that link: "Theorems are results proven from axioms, more specifically those of mathematical logic and the systems in question. Laws usually refer to axioms themselves, but can also refer to well-established and common formulas such as the law of sines and the law of cosines, which really are theorems." -user4594
