Proof by Contradiction | Explanation + 5 Examples

In this video, I explain the basic idea of the proof by contradiction method. Then I show 5 examples of using proof by contradiction to prove some propositions.
Thanks for watching! Comment below with questions, and make sure to keep flexin' those brain muscles!
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[@luketrebisacci2754]

VERY disappointed. In the thumbnail, I was promised FIRE. I expected you to hold and bend fire while teaching me pre calculus. I am unsubscribing and disliking this video.

[@BrainGainzOfficial]

LOL :D

[@kingfisher7360]

Now that was an effective video. I had almost given up, but this made it so easy. Thank you!

[@peter4844]

I watched 3 different videos before coming here. Yours by far did the best explaining. I followed along with a similar problem and got my answer successfully :)

[@loveconomics]

What an amazing video. Clear and concise. Thank you!

[@kaniarisjad8123]

this by far the most helpful video. thanks!

[@nightshade7092]

The chalk board sounds are so satisfying! I have my P4 A level mocks in a few hours, very well prepped but always found proof difficult, but not so much after this video! Thank you very much

[@AshishSingh-753]

Hey Andrew keep it up your content heal the pain of abstraction of concept

[@user-qi4fq3gz6d]

That simplicity in your explanation and the aura on you are gooooood...Thank you...I have subscribed

[@LemuelYeboah]

The explanation is really simple Thanks

[@TwoTerrificTails]

SUPER helpful, thank you!!!

[@iraklimikadze9950]

This video helped me a lot. Thanks!

[@manavpatelpatel9735]

I personally love this video it was wonderful. I'm liking this video.

[@RubiMercuri]

thankyou so much this video helped more than i expected!

[@melinawettstein4361]

i’m taking a midterm on proofs today so this video was perfect timing

[@BrainGainzOfficial]

GL! :D

[@frederickteye]

Thank you chairman

[@jdmoon9533]

Simply amazing!

[@axelletougouma8792]

You are the best 🤗🎊

[@christophershaba2492]

i like your stuff bro and im really flexing my brain muscles

[@RENCIOL]

Nice vid!

[@rigbyb]

Great video, thanks a lot

[@prosperademoye7713]

Thank you so much this really helped me in my exam

[@ruantristancarlinsky3851]

Man you really helped me out a lot bro, you explained really well and I kinda like math a little more now😂👌

[@BrainGainzOfficial]

That's great to hear!

[@justinotherpatriot1744]

Well, this was awesome.

[@user-zv1pp4yj8k]

Well explained 👏

[@takondwatanganyika5203]

So helpful..thanks

[@maxhmetonxrono]

Man GG the best ty !!!!

[@mushfiqshahriar6454]

tnx a lot sir it really helped

[@kirimievansgitonga3449]

the video was very awesome🥰🥰🥰🥰

[@jshringo77]

you are the goat

[@user-fv7yl7xi9j]

Thanks bro

[@segfault1361]

The third and fourth proofs can also be proven by contrapositive

[@Phoenix-cg3hq]

that was helpful

[@RS-xu1dm]

Is this correct for the last example? >> a^2 = 4b +2 and then a = sqrt of 4b +2. and after taking square root by plugging in values for b, a = a decimal number. Hence a is not an integer. So our assumption is not true.

[@MalkoleBG]

thank you

[@user-qi4fq3gz6d]

can we assume negation of p to be false and by contradiction run to be true and conclude p is false?

[@tibrummichael2715]

God bless you

[@yamatanoorochi3149]

~(p->q) is p and ~q So 3n + 7 is even and n is even (Matches with contrapositive?) 3n + 7 = 2k where k is any odd integer and n = 2m with m being any odd integer 3(2m) + 7 = 2k 6m + 7 = 2k 7 = 2(k - 3m) Spz a number g = k-3m 7=2g Implying that 7 is even, which is a contradiction Hence the original statement is true Would having 2 different odd integers be false? Thanks

[@karengracebaniwat6573]

sir? how about using proof of contradiction, for all real numbers x, if x is irrational, the -x is irrational..

[@Flux281]

hi, do you have videos on predicate logic ?

[@hannanmulla7623]

there may have been a small mistake in the truth table where p is F and q is T. I think (p->q) should be F. and (p^~q) should be T.

[@jehoshaphatjimmy4069]

How can we prove my contradiction that the world is round?

[@yamatanoorochi3149]

Damn right I'm gonna flex em

[@meanderer9808]

this is proof by contraposition

[@ChrisInTheNorth]

I'm not sure all of these need the contradiction formulation to prove

[@nandinireddy779]

Awww!! So handsome i watched u throughout the video instead of listening

[@swornimdangol5387]

I assume you want the proof explained in a little more detail. Here's what the proof says in English. Lets assume that conditions 1 and 2 hold. We use a proof by contradiction that it must be true for all n>=1. As with all proofs by contradiction, we assume the statement is false and then show it leads to a contradiction. So we assume there is some s for which P(s) is false. Lets pick the smallest s where P(s) is false. (We know that there must be a smallest number s where it is false, because any non-empty set of natural numbers must contain a smallest value). But we know that P(s-1) is true (because s is the smallest value where P(s) is false, and s-1 is less than s). But if P(s-1) is true, then P(s-1+1) = P(s) is true, contradicting our assumption that P(s) is false. Therefore there cannot be any s where P(s) is false. The s-1 finds the number immediately before the rule supposedly breaks down. But we know that if P(s-1) is true then P(s) must also be true, because of condition 2. This contradicts our assumption that the rule doesn't hold for P(s). Well-ordering appears explicitly when we use the fact that any non-empty collection of natural numbers (in this case the collection of natural numbers x where P(x) is false) must have a lowest number. More generally, the well-ordering principle states that if you consider 1,2,3 ... then this list will contain all natural numbers; there are no natural numbers that cannot be reached by starting at 1 and adding 1 repeatedly. If there were any missing numbers (ie if the set cannot be well ordered) then proof by induction would not work.

[@hindabdullah6470]

انتا مُزه ي استاد

[@shauny4596]

but you are handsome. how is a handsome man like you became so smart ?

[@EpicMathTime]

This dude thinks he's fancy with his 60 fps

[@plsletmomodrive]

wait omg why is he so hot... i dont hate discrete math as much anymore...

[@Loots1]

thats a 2? nah bro thats a z lol

[@user-ix7nx7pz9m]

Your explanation is too fast can you slow it down please

[@Abhinavkumar-og3xd]

Please speak in hindi.