You assume the statement is true. For any natural number k the statement works. So IF the thing you assumed is true, then the statement also works for k+1. Therefore, since you have already proven that k=1 works, your assumption is correct. And therefore you can conclude the statement works for 2, 3, 4... Assuming that the statement is true is vital in this case.

Halfway through the video and all I keep thinking is, "So this is what people have to deal with watching me write something left-handed? My hand covering up what I'm writing until I'm done?"

You have literally taught me in 6 min what I have spent up to 10 hours learning from my professor, textbook, quizzes, and assignments. You r the best TheXvid tutor. Thank you

Lol, this may seem weird but I find it satisfying to watch and learn from Left-handed mathematicians. Their hand usually is in the way of some of the problem whilst writing it out, therefore, it gives me the logical reason of being last to answer for being the only one to go back and read the problem once more. â˜º

18 seconds in; got some glimpse of some of the hint of the gist of the depth; laughed hard, kept watching on, finished the vid, wrote this comment, went on with my mediocre hair day to ongoing presents.

Induction must be the least elegant type of proof. We are assuming to much. And of course the result will end up correct. P(m) + X will always add up to P(m+1)

Patrick I'm sure you get a lot comments praising you so instead just get yourself an ice cream for your well put explanation on the concept of proof by induction.

James 2: 6-7 But you have dishonored the poor. Is it not the rich who are exploiting you? Are they not the ones who are dragging you into court? Are they not the ones who are blaspheming the noble name of him to whom you belong?

syed saba4 days agoAmazing.. Video ðŸ‘ŒðŸ‘ŒðŸ‘ŒðŸ‘Œ

Inayat khan6 days agoperfect

Garen Kantarci7 days agoHas anyone told you that you are a god among men?

mqhele mguni22 days ago2019 at PJMT BUSE University says Patrick is the TRUTH!

patrickJMT22 days agopreach it!!

Simi S28 days ago^{+1}Anyone noticed that he is left hand ed

patrickJMT28 days ago^{+1}ed, he is left hand.

Greggie Pattry2 months agodo i always assume the statement is true?

Lars KMonth agoYou assume the statement is true. For any natural number k the statement works. So IF the thing you assumed is true, then the statement also works for k+1. Therefore, since you have already proven that k=1 works, your assumption is correct. And therefore you can conclude the statement works for 2, 3, 4...

Assuming that the statement is true is vital in this case.

Thifal Raniah2 months agoThank you so much! ðŸ”¥ðŸ’›

Sunil nair2 months ago^{+1}Tnx sirðŸ˜ŠðŸ˜Š

Josh Lipovetsky2 months agoThank you!

stellus francis3 months agoThnx a lot.......

Helen Jay3 months agoThank you very much for this video I'm doing my maths exam revision now.

arletd paucar4 months agowow I didn't get it until I saw your video! very helpful

Frank V4 months agoHalfway through the video and all I keep thinking is, "So this is what people have to deal with watching me write something left-handed? My hand covering up what I'm writing until I'm done?"

Sebastian Suarez4 months agoWhy do you add 5(k+1)-1 to the left side and not just 5(k+1)??

Helen Jay3 months ago^{+1}The K plus 1 was shoved into the equation.

Elvin Gamers4 months ago^{+1}Hello 2010

Stephen Mack4 months ago^{+2}Your videos on induction, partial fraction decomposition, and derivatives are saving my life before finals rn tysm

Landon Shenberger6 months agoTHANK YOU

Divya Shukla6 months agoG

PicledH6 months agowhat is the additional term for??

Queso Dilla6 months agoToo bad this would get me marked in my class as my teacher counts 0 as a natural number which disproves the base case lol

crissy newton hwaaa6 months agothis is simply the best keep on keeping on

Fade6 months agoGoddamn, I should've watched this video instead of rereading the same section from the textbook for hours.

Sam Saghafi7 months agoYou have literally taught me in 6 min what I have spent up to 10 hours learning from my professor, textbook, quizzes, and assignments. You r the best TheXvid tutor. Thank you

Nigel Sterne7 months agoIve been searching for hours and this is the only vid that made sense, thanks!

Chuyu Liu7 months agoThank you

Joseph G. Hotto9 months ago*breathes a sigh of relief*

Victor Tsenov10 months agothank you kind sir.

ToXiiC NebuLa10 months agoLol, this may seem weird but I find it satisfying to watch and learn from Left-handed mathematicians. Their hand usually is in the way of some of the problem whilst writing it out, therefore, it gives me the logical reason of being last to answer for being the only one to go back and read the problem once more. â˜º

Xylok10 months agoi bet i can become three times better at math than you before you can eat and transform into nothingness a full size universe!

Xylok10 months ago18 seconds in; got some glimpse of some of the hint of the gist of the depth; laughed hard, kept watching on, finished the vid, wrote this comment, went on with my mediocre hair day to ongoing presents.

ORACLE OFFICIAL10 months agoi'll teach you to be right handed cz your left hand really really really sucks..!

aeroO bics11 months ago^{+1}Induction must be the least elegant type of proof. We are assuming to much. And of course the result will end up correct. P(m) + X will always add up to P(m+1)

n n11 months agoWow couldn't be any easier

Eric MeyerhuberYear agoNice clear example and explanation. I knew it wasn't hard, but the book and prof did not do what you did. Thank you very much.

Meg AnedezYear agoPls answer me why thereâ€™s additional i dont get it

Antonio J G-BYear agoPatrick I'm sure you get a lot comments praising you so instead just get yourself an ice cream for your well put explanation on the concept of proof by induction.

Antonio J G-BYear agoI'm confused as to why he went from 4+9+14+19+...+(5k-1) into (k/2)(3+5k)

Antonio J G-BYear agoI figured it out, he replaced it because we substituted with the P(k) expression from our assumption.

THE ROYALSYear ago^{+2}sir where is 13k coming from and why

Nemisha ChrisYear agoWhy we adding additional term in left hand side

Karabo MonaiwaYear agoYet you save my life again...

Honey Claire GemenianoYear agoI dont get it. Sorry for my stupidity

Twisting TigerYear agoI wish he wasn't left-handed. His left hand acted as a barrier ðŸ˜•

patrickJMTYear agoyea, it does get in the way sometimes. i try to be conscious of it but often forget

Dexter NicerYear agowhere did you get the times 2 in 4k/1?

Ahmed MirzaYear agoWhere is 5k gone plzz tell me

Yousif SirriehYear agomnwer ya gale

Darknavy42Year agoExam is in 30 minutes and yet again, I learn more from you. Cheers

Aimee W.Year agojust want to let you know that I'm in love with you.

patrickJMTYear ago*hugz*

Blo opYear agoDeyam

Warren BinderYear ago8 years later, thank you!

Robert WagnerYear agoGood stuff

Chandru .AYear agoWe should write in your right hand

sophie ng seahYear agouseful video! Thumbs up!

Nicholas HendersonYear agoMy discrete math assignment thanks you

Pedro TorchioYear agoNaturals bigger than zero, right? Or are you considering Natural numbers as positive Integers? Thanks for the vid

siyethemba simlindileYear agowhenever im searching a topic on maths i include Patrick at the end just for em to take me straight to ya, ya are the best. thank ya

patrickJMTYear agothanks! :)

Jack DanielYear agoDamn, your writing is so clear and fast!

Proper way to live by givingYear agoJames 2: 6-7 But you have dishonored the poor. Is it not the rich who are exploiting you? Are they not the ones who are dragging you into court? Are they not the ones who are blaspheming the noble name of him to whom you belong?

Caspar ClaessenYear agoThanks a lot because of you I have courage and hope that I will pass my exam tomorrow

Kameryn CherryYear ago^{+13}math makes me want to die. Your explanations make me want to die less. thanks lol

Huckleberry LoverYear agoThanks!