Fun Fact: Mathematical Induction is actually a deductive method of proof. Mathematical induction is different from logical induction. I’ve written quite a lengthy paper on this topic (while I was an undergrad studying mathematics). Lmk if you’re interested in reading it!
On 4:59-5:12 I couldn't quite understand what he said when he stated what type of series the problem can only be solved through, i had even checked closed captions and the provided transcript but it showed a asthmatic sequence. can someone help
He just says you must know Arithmetic series to complete this, also that you will learn how to do it with other series later once you have learnt it. That’s what I think he meant but I am not 100% sure as I am only able to do arithmetic series at the moment as well.
Yeah, so basically he was saying that the formula for arithmetic series only works...because it is an arithmetic series. He was trying to show proof by induction's helpfulness, despite just having shown that you can easily prove the example through deduction. It wasn't too important; all it really meant was that proof by induction is useful to know because sometimes it's all you can use/the best method.
I had a maths teacher like you last year but now I've moved schools and my teachers aren't as good and the only way I am surviving is by watching your videos thanks Eddie Woo
I've known how to do induction for ages, but I was never able to do it because (ironically) I didn't understand how you could just "assume" n=k is true, and consequently I assumed there was something I was missing. Turns out you literally just assume it.
Thank you sir! I really love your teaching method. I understand even in one time, which I couldn't understand when my professor go through even 3 times.
I have a question: Wouldn't the next number after 2k - 1 be 2k? Therefore making the prove part: 1 + 3 + 5 + ... + (2k - 1) + (2k) = (k^2 + 2k) or 1 + 3 + 5 + ... + (2k - 1) + [(2k - 1) + 1] = (k^2 + 2k) The way I see he added 2 to (2k - 1), but isn't it supposed to be the next number after 2k - 1, namely, 2k? It's at 11:35
2n - 1 is the general formula for every odd no. 2n - 1 IS NOT EQUAL TO n^2 But summation of 2n -1 is. That means the sum of n odd nos is equal to n^2. For example, if n = 2 We put n = 2 in the equation - sum of 2 odd nos = n^2 = 2^2 I have the first 2 odd nos i.e. 1 and 3. Now 1+3 = 4 Also we had n = 2 and so n^2 is 2^2 which is 4. So 1 + 3 + 5 +...+ (2n-1) = n^2 is a general equation where n odd nos. When added give the sum as n^2. Hope it helps.
Thanks ! Are you on skype? I have a few simple questions, and I am confident that you will be able to answer. Thanks. (I am writing a test next week Friday i.e 06/03/14) a reply in this regard would be appreciated! Thanks again for the helpful lesson.
Induction proof multiple variable method. 1)Show that it's true for the smallest concrete case (anchor case). 2)Assume it's true for the general case. 3) Logically prove that if it's true for the general case then it's true for all next general cases. 4)Explain that the variables can be assigned values of the concrete (or anchor) case
To the world you might be just a teacher but to me..........your a hero
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thanks Mr Eddie Woo, you just save me tons of energy and time. Your explanation was an eye opener for me to mathematical induction.
You are an amazing teacher! Thank you for doing what you do!
17:45 "and if u wanna be a real nerd heh u can say.." i love this
with Eddie it looks so simple :) thanks a lot!
Thank you Eddie! This was very helpful.
Great explanation, exactly what I had issues with! Thank you!
Thank You! Great Lecture!
Can u teach us Strong Mathematical Induction?
Fun Fact: Mathematical Induction is actually a deductive method of proof. Mathematical induction is different from logical induction. I’ve written quite a lengthy paper on this topic (while I was an undergrad studying mathematics). Lmk if you’re interested in reading it!
interested
I can understand this video better than the video they provided on my online course...
Great job! Extremely clear and concise.
this helped so much did know induction can be this easy
You are excellent teacher
Hai sir iam from India 🇮🇳 thank you sir
Eddie Woo GOAT fr
You are adorable !
You are the best!
Quick question. Why didn't you use the whole term on the L.H.S to test since its not just (2n-1) equating to n squared.
Your students are really lucky..You make it so simple to understand.
Best teacher ever.
Could I have an email to personally send me questions to?
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why do i attend university
Not all heros wear capes, some wear sweater vests.
very helpful, thanks
this guy is even better than my prof in u of t
Can you prove a physics or economics formula with mathematical induction? Can u make a video of it? 😃😀
that duster is soo cool.
Thank you so much!
You are soo energetic and good teacher.Are you from China.If it then I want to go to China for study
excellent job
Eddie you seem like a very good teacher but the whiteboard is too far away from the camera.
On 4:59-5:12 I couldn't quite understand what he said when he stated what type of series the problem can only be solved through, i had even checked closed captions and the provided transcript but it showed a asthmatic sequence. can someone help
Arithmetic
He just says you must know Arithmetic series to complete this, also that you will learn how to do it with other series later once you have learnt it. That’s what I think he meant but I am not 100% sure as I am only able to do arithmetic series at the moment as well.
Yeah, so basically he was saying that the formula for arithmetic series only works...because it is an arithmetic series. He was trying to show proof by induction's helpfulness, despite just having shown that you can easily prove the example through deduction. It wasn't too important; all it really meant was that proof by induction is useful to know because sometimes it's all you can use/the best method.
I'm an engineering graduate and I've never been able to understand induction... That changes today. Good teachers are gods.
This teacher is single handedly saving millions of students💪 Eddie Woo is the man fr
thank you!! you explain it better and more concisely than my compsci prof
Literally sitting here in my car after my discrete structures lecture and this man just made it click
I thought he was asking for Dominoes pizza
Concise, Easy to Understand, Enthusiastic... Amazing.
I'm in a maths degree and this explanation is fantastic. :D
You should come to Ghana...we seriously need lecturers like this who don't make us sleep😭😂
this is the best and easiest explanation of mathematical induction I have ever come across. thanks teacher Eddie
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I LOVE EDDIE WOO!!!!!!!!!!!!
You're an Amazing teacher Mister woo!
I loathed maths. I love it now.
One teacher to another ... 👏
Just out of interest...is your class always lecture form and do you not like use of technology, gimmicks etc?
I had a maths teacher like you last year but now I've moved schools and my teachers aren't as good and the only way I am surviving is by watching your videos thanks Eddie Woo
I just realised how beautiful proof by induction is
I wish you were my mark teacher. You explain a lot easier. best teacher for me.
thank you so much, i can't explain how much your videos have helped me 😭
I've known how to do induction for ages, but I was never able to do it because (ironically) I didn't understand how you could just "assume" n=k is true, and consequently I assumed there was something I was missing. Turns out you literally just assume it.
bruh I actually get goosebumps if i watch this guy's video
my teacher taught this in like five minute, so can bearly understand, thanks to this class now i know
Strong mathematics induction and weak form...
The explanation was good but he made a mistake 😅. 2n-1 is not equals to n^2
why is he teaching me better than my specialist teacher?
Just too good 👍
Awesome stuff professor very easy to understand now :)
G, thanks. That's all I can say.
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I am grateful Mr Woo Mathematics teaching never able to grasp Maths easily
Thank you sir!
I really love your teaching method.
I understand even in one time, which I couldn't understand when my professor go through even 3 times.
Ok I think I like it here, easy to understand, makes jokes that keep u engage, hot teacher
You explained it like a friend🥲Thank you so much
what if they say
For all n ≥ 1:
n
∑ (2i -1) = n^2
i = 1
What do I do with the i?
This was so helpful! Thank you for sharing.
I hope you will continue your video, it's so clear and concise
amazing! thank u >>> very helpful
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Brilliant, thanks Eddie.
Love it! keep going sir.
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Gigachad teacher
Great lectures, keep it up!!
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i love you
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Brilliant
I have a question: Wouldn't the next number after 2k - 1 be 2k? Therefore making the prove part:
1 + 3 + 5 + ... + (2k - 1) + (2k) = (k^2 + 2k) or 1 + 3 + 5 + ... + (2k - 1) + [(2k - 1) + 1] = (k^2 + 2k)
The way I see he added 2 to (2k - 1), but isn't it supposed to be the next number after 2k - 1, namely, 2k?
It's at 11:35
It's a series of odd numbers, hence next number is +2 from previous one(not +1).
@@hmm1778 Oh yes, of course, forgot about that. Thanks.
@@hmm1778 yeh but 2n-1 does not equal n^2
In which institute are u teaching .?u r the best
thank u soooo much... ur a very good lecturer
why is (2n-1) = n ^ 2 ?
2n - 1 is the general formula for every odd no.
2n - 1 IS NOT EQUAL TO n^2
But summation of 2n -1 is.
That means the sum of n odd nos is equal to n^2.
For example, if n = 2
We put n = 2 in the equation - sum of 2 odd nos = n^2 = 2^2
I have the first 2 odd nos i.e. 1 and 3. Now 1+3 = 4
Also we had n = 2 and so n^2 is 2^2 which is 4.
So 1 + 3 + 5 +...+ (2n-1) = n^2 is a general equation where n odd nos. When added give the sum as n^2.
Hope it helps.
great work dude...
Thanks ! Are you on skype? I have a few simple questions, and I am confident that you will be able to answer. Thanks. (I am writing a test next week Friday i.e 06/03/14) a reply in this regard would be appreciated! Thanks again for the helpful lesson.
oof
Induction proof multiple variable method.
1)Show that it's true for the smallest concrete case (anchor case).
2)Assume it's true for the general case.
3) Logically prove that if it's true for the general case then it's true for all next general cases.
4)Explain that the variables can be assigned values of the concrete (or anchor) case