Some things that were not clear to me, can some one help me out with them?
1) While representing 1+1 = 2 i.e (= (+ (next 0) (next 0)) (next (next 0))) which comes at the start of this article, is this considered to be just a statement? Or a true statement that follows from the axioms?
2) On formulas, this example is shown (there-is a (= (next 0) a)). It is not clear whether this is a necessarily true statement or some symbols relating a and 0.
3) He says that proofs are a sequence of formulas but colloquially they are sequence of "implications". That "implication" is introduced later on and it is shown that this "implication" symbol also needs to be proved (successor). Didn't he use the fact that one thing implies another multiple times previously?
I need the distinction amongst "statement", "formula" and "axioms".
Apologies if the above looks like a vegetable soup but I'd love some explanation for this.
1) While representing 1+1 = 2 i.e (= (+ (next 0) (next 0)) (next (next 0))) which comes at the start of this article, is this considered to be just a statement? Or a true statement that follows from the axioms?
2) On formulas, this example is shown (there-is a (= (next 0) a)). It is not clear whether this is a necessarily true statement or some symbols relating a and 0.
3) He says that proofs are a sequence of formulas but colloquially they are sequence of "implications". That "implication" is introduced later on and it is shown that this "implication" symbol also needs to be proved (successor). Didn't he use the fact that one thing implies another multiple times previously?
I need the distinction amongst "statement", "formula" and "axioms".
Apologies if the above looks like a vegetable soup but I'd love some explanation for this.