Syntax of first order logic.
... Mathematical approach: Work towards an axiom system of mathematics with purely mathematical means. (Hilbert’s Programme). In its naïve interpretation crushed by Gödel’s Incompleteness Theorem. Extra-mathematical approach: Use external arguments for axioms and rules: pragmatic, philosophical, sociolo ...
... Mathematical approach: Work towards an axiom system of mathematics with purely mathematical means. (Hilbert’s Programme). In its naïve interpretation crushed by Gödel’s Incompleteness Theorem. Extra-mathematical approach: Use external arguments for axioms and rules: pragmatic, philosophical, sociolo ...
A,B
... (a1, a2, a3, …. an) is identical to (b1, b2, b3, …. bn) if and only if ai = bi for all i= 1 …. n) In other words, elements must match, in order. Clarifying – {2,3} and {3,2} are the same set, but different tuples – {2,2} and {2} are the same set, but different tuples You will remember ordered 2-tupl ...
... (a1, a2, a3, …. an) is identical to (b1, b2, b3, …. bn) if and only if ai = bi for all i= 1 …. n) In other words, elements must match, in order. Clarifying – {2,3} and {3,2} are the same set, but different tuples – {2,2} and {2} are the same set, but different tuples You will remember ordered 2-tupl ...
The Axiom of Choice
... order on the integers Z is not a well-ordering: choose any subset which is not bounded below, e.g. {0, −1, −2, . . .} (or for that matter all of Z), and such a subset will not have a least element. However, you can come up with a different total ordering of the integers which is a well-ordering; fo ...
... order on the integers Z is not a well-ordering: choose any subset which is not bounded below, e.g. {0, −1, −2, . . .} (or for that matter all of Z), and such a subset will not have a least element. However, you can come up with a different total ordering of the integers which is a well-ordering; fo ...