The best presentation on the web of a topic many find confusing. Do you offer on-line assistance on questions of logic? You would make an excellent tutor.
Forgive me but at [4:10] why is one allowed to assume all the steps from P(1) all the way to P(k) are true? This is the only part of strong induction I don't understand. I have scoured RUclips and the internet for an explanation but cannot find one. Everyone just says you can assume it but I haven't found an explanation as to why. Thank you to anyone who can explain this in simple terms.
If the base case P(1) is true( this can't be assumed,it has to be true),then if you prove the general induction (considering arbitrary K): If assuming all from P(1) to P(K-1) is true and you prove P(K) also is true,then you can build P(2) from P(1), P(3) from P(2) and P(1) and so on.. This is strong induction cuz your P(K) can depend on any state from P(1) to P(K-1).In most of the abstract alegbra proofs,the state which P(K) depends on can be arbitrary but you know it's less than K,so you can you use the induction assumption. (If you are familiar with CS algorithms,this is similar in essence to dynamic programming)
waste of my time imo, its great that youve shown the conclusion of strong induction. but if you already knew the induction step was true then you didnt need this video.
Im in tears right now, 1 month trying to understand this god bless you
what an incredible teacher! your explanation are really straightforward which makes my discrete math course just so so much easier
incredibly useful video, your explanations are extremely straightforward and easy to follow. Also, i like the editing style of this video :)
This deserves a million views and likes
this is so underrated...
yes indeed
thank you 🥺🥺 you're awesome!!
Very useful video , i like your explanation style
best video on this topic, thanks!
U explain stuff so well Fr girl
Great video .
Amazing teaching
Excellent video lecture.
The best presentation on the web of a topic many find confusing. Do you offer on-line assistance on questions of logic? You would make an excellent tutor.
Forgive me but at [4:10] why is one allowed to assume all the steps from P(1) all the way to P(k) are true? This is the only part of strong induction I don't understand. I have scoured RUclips and the internet for an explanation but cannot find one. Everyone just says you can assume it but I haven't found an explanation as to why.
Thank you to anyone who can explain this in simple terms.
If the base case P(1) is true( this can't be assumed,it has to be true),then if you prove the general induction (considering arbitrary K): If assuming all from P(1) to P(K-1) is true and you prove P(K) also is true,then you can build P(2) from P(1), P(3) from P(2) and P(1) and so on.. This is strong induction cuz your P(K) can depend on any state from P(1) to P(K-1).In most of the abstract alegbra proofs,the state which P(K) depends on can be arbitrary but you know it's less than K,so you can you use the induction assumption. (If you are familiar with CS algorithms,this is similar in essence to dynamic programming)
Thank you for the video
Very helpful thanks
how he is standing at back and writing ..(just being curious)
The video is mirrored. Notice that most people that do this appear to be writing with their left hand when 90% of people are right handed.
@@ziquaftynny9285 that makes more sense I was like "how is this dud writing everything perfectly backwards" lol
waste of my time imo, its great that youve shown the conclusion of strong induction. but if you already knew the induction step was true then you didnt need this video.