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JustAGuyWhoLikesMath
США
Добавлен 9 янв 2020
This channel is meant to discuss mathematics concepts and solve related example problems. I've always enjoyed learning about math, and I'll teach you that it isn't really that hard!
Prove that sum of the first n odd numbers in equal to n squared
Using the Principle of Strong Math Induction, or PSMI for short, learn how to prove that the sum of the first n odd numbers equals n squared!
Просмотров: 2 675
Видео
Principle of Strong Math Induction (PSMI)
Просмотров 1714 года назад
Learn about the PSMI and the two steps required to prove propositions!
Hallway Tile Problem
Просмотров 364 года назад
This is a fairly complicated problem which uses the Euclidean Algorithm to find out how many tiles of a certain length can fill up an entire hallway perfectly (no fractions, no remainders). However, once you understand it, it is easy to apply the knowledge elsewhere with different types of problems. Hope this help! =)
Converting Repeating Decimals to Fractions
Просмотров 624 года назад
In just three steps, you can convert a repeating decimal to a fraction! Learn how to do so in this video, in which I give four examples of increasing difficulty so you can handle any problem of this type that comes your way!
What is Weighted Average?
Просмотров 214 года назад
In this video, I talk about weighted average, give a couple of examples about cost & quantity and speed & time, and I also explain why we need to use weighted average. I hope this helps! :)
Prove Square Root of 6 is Irrational
Просмотров 19 тыс.4 года назад
Learn how to prove that the square root of 6 is irrational! Using this method, you can actually prove the square roots of any non-perfect squares is irrational, all that happens is that the numbers change a bit. Regardless, the process is the same, and the end result is (obviously) the same.
Unique Factorization Theorem
Просмотров 18 тыс.4 года назад
Learn the proof of how every number can only be represented in a unique way from prime factorization!
Every natural number can be expressed as a product of primes proof
Просмотров 9 тыс.4 года назад
While this may seem trivial, the proof is quite interesting. Learn how every natural number can be expressed as a product of primes!
The Set Of Real Numbers Is Uncountable
Просмотров 15 тыс.4 года назад
In this video, I show you one of my favorite proofs - R is uncountable. Find out what uncountable means and how the set of real numbers is uncountable!
Bezout's Lemma
Просмотров 744 года назад
The Bezout's Lemma is quite a difficult lemma. In this video, I try to break it down and explain the proof. Let me know if this helps!
GCD Characterization Theorem with examples
Просмотров 5244 года назад
Learn the GCD Characterization Theorem with the examples and counterexamples in this video. I also show the proof for this theorem in this video.
Euclidean Algorithm with example
Просмотров 1354 года назад
The Euclidean Algorithm helps find the greatest common divisor of two numbers in a matter of seconds. Learn how to use this algorithm from this video!
Prove that when a=qb+r, gcd(a,b)=gcd(b,r)
Просмотров 8 тыс.4 года назад
This proposition is the basis of the Euclidean Algorithm. Learn how for a=qb r for any a,b,q and r belonging to Integers, the gcd(a,b)= gcd(b,r)
Prove That There Are Infinite Primes
Просмотров 1494 года назад
Check out one of my favorite proofs! There are infinitely many primes, and this video proves just that. Bonus fact: The largest known prime number to this date is (2^ (82,589,933)) − 1, a number that has 24,862,048 digits when written in base 10!c
Trailing Zeroes And Power Of A Prime In A Factorial
Просмотров 884 года назад
Learn how to find the number of trailing zeroes in a factorial and find the power of prime p in a factorial as well. While this might seems difficult at first, it is quite easy, and if you remember one simple formula (and maybe even the reasoning), you can get the answer for any number in no time!
How To Get The Last Digit Of Any Number Raised To Any Power
Просмотров 2584 года назад
How To Get The Last Digit Of Any Number Raised To Any Power
Bro , even pw can't made me understand this question and you did .. so heads off to you underrated man 🫡🫡
Is it possible to prove it, showing that both a"" and "b" are even?
Not a good, concise proof, proof by induction is clearer
Since we know that d divides a - qb, we can say that dm=a-qb for any integer m and hence we can say that a = dm + qb and dm is obviously an integer and our theorem is proved!
What you said doesn't make sense.
Isk threesteps hota ha jnb
@ 2:54 not d=gcd (b,r) but d=common divisor (b,r)...I suppose
Uniqueness??
you explained so simply, thank you !!
Please, why's c a number 1 - 8 and not 0 - 9
That doesnt explain anything. You jumped when you went into it sufficed and why is cla mean c<=d
the more generalized proof should consider the number of p's and q's to be not equal.. Cheers for this excellent proof though
This video is more for you to show off, rather than to considerately explain anything.
thanks for your kind information.
Good
Thank you very much I found the proof to be quite beautiful
WHEN n = 1 it is also a natural number but 1 cannot be expressed by product of primes. Therefore, the statement is wrong
Thank you I finally understand
my brother u are a great teacher. really helpful. Ik I'm the first and only commentor, but trust me this channel deserves more.
In India this is a hard question for 10th Grade students
I guess you could consider which 10th graders, but I would say that this question would be hard for most high school students in the United States. From my experience.
Real
you are so cool. Thanks for the video
I just want to say, this is such an underrated channel. Wish you kept making videos
perfect thanks boss
Thanks for the explanation! You're a lifesaver!
Nice explanation. I only felt that the "divides any linear combination" part could have been more rigorously proved, but I don't mind, since that part is very intuitive to me. I think there are many explanations of this proposition online that try to be more succinct, but end up not proving intermediate steps, or even worse, not realizing that something needs to be proved or using circular reasoning.
Suppose gcd(a,b) = g such that a/g = c, b/g = d Now if we multiplied a/g and b/g by some factor x and y respectively we’d get ax/g =cx, by/g = dy, adding them simultaneously you would get ax + by = g(cx + dy) which is completely divisible by g. Hence any linear combination of a and b would be divisible by g.
@@ceiro4467 Thanks Buddy ! I was scratching my head to understand that !
thanks for the explanation
Hi. You appear to be assuming that the sets of P and Q primes have the same number of elements, namely N. For a more rigorous proof you should start with (for instance) a set P with i elements and the set Q with j elements. You, thoughout the course of the proof, show that i=j.
How can you assume p1, p2, p3.. and q1, q2 , q3.. are both made up of N elements. There is loss of generality with this assumption.
How Show that gcd(ab,m)|gcd(a,m) gcd(b,m)?
Great proof thanks a lot :)
Bhai vimal thuk kr banata video
It’s his accent bro wdym
Just Damn it , It's so Op
Thanks indeed bro.
Weldon
thank you for this!
Very straightforward, thank you sir!
thanks a lot, guy who likes math, I needed to know this so much
this was literally my exam questions last semester lol
100th subscriber! :)
i didnt get the meaning of GCD
I think it means greatest common denominator
@@kaidenfoley4041 No it's greatest common divisor it was taught in our school
Hey , can u explain this part (1:37 ) please
The step at 2:39 is completely unjustified. Moreover, it does not hold for other number systems, which means we cannot simply assume it to be true.
this is exactly the step which I am trying to get an explanation for and the video I find just skips over it.
@Muhammad Ashraf what do you mean by “1<q<i”, there are no values “i” and “q” in this proof. There is “q_i”, but it is rather obvious that 1 < q_i.
@Muhammad Ashraf what do you mean by “1<q<i”, there are no values “i” and “q” in this proof. There is “q_i”, but it is rather obvious that 1 < q_i. Also, I don’t know what you think it must divide, since you only gave an inequality and no values.
I do not understand why p has to divide qi (just before 3 minute mark)
If p is a factor of (a * b* c * …..) and a,b,c,… are all prime then p is a factor of those primes. This has to be true for p to be a factor of the product of primes: it needs to divide into one of the primes.
Also prime no. Cannot be expressed as product of primes
Yes, I spotted that too, unless you consider 1 to be prime, which it is not.
Nice
Hilbert’s Hotel will always have rooms for countably infinite guests. The set of real numbers, however, is uncountable. What issues can come up for a Real Infinite Hotel? Reply real quick
Hey, that was a good explanation. Also, don't be so hard on yourself. Communicating maths can be a lot harder than learning it. You will find you get a better understanding of things if you teach it to others.
Good fucking video, my prof turns this 2 minute video, 30 mins of lecture time
That set isn’t finite.
Isn't this called *The Fundamental theorem of Arithmetic* ?
Yeah lol
This is the only video on RUclips which covers this preposition... Thanks a lot.. I established everything myself but I don't know why I wasn't able to complete the proof...
why does 3 divide 2b^2?
true, there was some ambiguity about this....
Because c^2 is an integer which is equal to 3 divided by 2b^2, hence 3 divides 2b^2.