The FAQ on proofs should emphasize definitions

[Stephen Tashi]

I think the FAQ on proofs would be improved if it emphasized the use of defintions. It says that theorems and axioms are used in proofs, but many many textbook type proofs hinge on "parsing" definitions correctly.

As alluded to in the FAQs related to "is .999.. = 1?", many difficulties that people have with proofs arise because they substitute their own mangled definitions of what things are in place of the actual definitions. For example, I notice that several forum members express a "Platonic" view of mathematical objects. They believe these objects exist independently of the definitions that mathematics makes for them. That may be fine as a general philosophy of life, but it is ineffective as an approach to writing mathematical proofs.

(I suppose this post falls under Science Education, but that section doesn't show a link to the math FAQs, so I posted here.)

 

[micromass]

Thank you for your wonderful comments, Stephen! You are certainly correct in saying that.
Could you perhaps post a possible improvement to the FAQ? That way we can integrate your comments.

 

[Stephen Tashi]

OK, I promise to post something in this thread, but it might take a few weeks. I'm a very busy man - retired, you know. It eats up all your time.

 

[Mark44]

I added that proofs use definitions and included lemmas as well. I also cleaned up the wording in two or three other places.