BM4. Methods of Proof

Basic Methods: We note the different methods of informal proof, which include direct proof, proof by contradiction, and proof by induction. We give proofs that sqrt(2) is irrational and that there are infinitely many primes, among others.

[dietzadelsbergg]

Dr. Bob thank  you for your crystal clear explanation of this matter!

[MathDoctorBob]

Thanks for the kind words, Julian! I'm just getting started. I just landed a full-time position at CUNY, and we're figuring out how to coordinate with regular curriculum now.

[Brams]

So few views, it took me a lifetime to find these VERY useful videos of yours, thank you! =))

[NnNnNn]

you have helped me in many courses, , much respect from saudi

[MathDoctorBob]

Proofs take a good deal of practice, and it helps to have an expert critiquing your style until you get the hang of it. This part of math is like learning a foreign language. (Not dumb, just not experienced yet. You wouldn't expect to be able to say anything in Chinese after only a few weeks, or months.)

[MathDoctorBob]

Formal proofs and theorems, yes. Google Formal Proof and John Harrison or Thomas Hales for short articles.

[abbiehowe]

Idk if you are still replying to comments, but I am confused by the induction example at 21.35 how does 2(j+k+1) make it a proof? I see how you got there, making k^2+k=j but i don't see how that shows anything?

[maxteer]

I've been struggling to tackle a proof that's very similar to the proof that there is no rational solutions for x^2=2. I'm trying to prove the same thing, but with 12 (No rational solutions for x^2=12). I'm not sure where I can make the right assumptions and how to get the algebra or logic to say this is true, though I've even seen root 2 proven irrational by using the Least upper bound theorem.

[TheAhernFamily]

MathDoctorBob Would be nice if you had some easier examples for us dummies that your lecture went a wee bit over our heads.. for example the method of contradiction with the prime number 2 was for me.

[JohnCuppi]

This video is really nice quality but I'm just really dumb and don't get direct proofs. I need it broken down further and explained like I'm stupid.