BM3. Formal Proofs

Basic Methods: We define theorems and describe how to formally construct a proof. We note further rules of inference and show how the logical equivalence of reductio ad absurdum allows proof by contradiction.

[blymark]

This is gold. The pace of your explanation is perfectly matched to the content. Incredible video.

[sophieelliott]

This is the best video explaining proofs i've found on the internet, thank you so much, you are saving my ass in logic this semester 😂😅😃

[marcelamuller]

The best explanation ever.... Many thanks!

[jarrodanderson]

I'm graduating in 2 weeks and I'm grateful to you for your wonderful videos.

[stevenan]

omg formal proofs are a living hell. however after watching this video you have made it that much more bearable. Thank you!

[christinebrun]

Congratulation Sir! You are realy professional!

[ivenousername]

Saved me just before my exam, thank you

[MathDoctorBob]

It doesn't, but the premises themselves do not combine in an obvious way to reach the conclusion. So we do work off to the side and insert some missing pieces. This takes practice. "Simplfication" is the formal name of this statement.

[MathDoctorBob]

@TheBobocum You're welcome, and thanks for the kind words! - Bob

[TheBobocum]

Your videos are great. Thanks for uploading them!

[MathDoctorBob]

You're welcome! I hear you. It's as fun as parsing sentences for grammar. But to do all the fun math, you need to speak the language.

[MathDoctorBob]

@Jessewb You're welcome! Admittedly it's a relief to only have to do it once here. - Bob

[luchadb]

I'm trying to solve the below, but i'm not sure if its right

prove S

1) (p -> q) premise
2) ¬p -> (¬q ^t) premise
3) (q v t) -> r premise
4) r -> s premise


5) p assumption
6) q from 1, elim ->
7) q v t from 6, intro v
8) r from 3, 7, elim ->
9) s from 4, 8, elim ->

so S is proving ???

thanks if your can answer

[mathmate]

what is the difference between formal and informal proof, Sir?

[DafranchYze]

Why do proofs of complex problems take so long? Is it because they require you to work from very basic axioms outlining all of your steps or is it that they require holding many abstract concepts in your head at once?

[charlesamofordjuoh]

Do you have videos on simplification? If not do you know a great site that has examples?

[amrabdelaty]

what book do you recommend?
Thanks for these amazing videos

[jansmith]

could you possibly do a video or explain how to do this problem? Let S(n) = ∑ μ(d)σ(d), where the sum is taken over all divisors d of n. Find a formula for S(n) in terms of the prime factorization of n.

[orangetransformer]

in the proof at 5:11 what did you do to take the first step and simplify Q ^ R -> Q?

[muhammadbaqir]

sir can you kindly do the steps for those proofs