Rational Numbers | Definition + First Proof

[@hpp6116]

You are an excellent teacher!

[@Salvation1984]

I looked at my class slides and got so frustrated cause I had no clue what it meant, watched your video, now everything is clear! Thank You!!

[@DrTrefor]

Glad it helped!

[@MrConverse]

4:21, (and a few additional times), you said that you’d get the lowest common denominator. You did get a common denominator, and that’s all you needed, but it is not necessarily the lowest.

[@andrewscott2791]

I go to ucla, paid something around 1k for this class to be confused, your video might be the thing that saves me.

[@lemushkairitu6492]

Thank you so much,your lectures saved me👏👏👌

[@devdin8157]

Almost halfway through the discrete math course, Thank you very much for these videos.

[@s_t_a_r__xyz9954]

Well done sir

[@sangurajeswari7191]

Tq you sir you solved my problem

[@tyziesyke5073]

You have saved a soul

[@webknowledge9989]

I watch these videos and then go to the book "Introduction to Algorithms" or CLRS and see how much more I understand.

[@avinashbajpai325]

Wow amazing to listen from you

[@vayramjosh]

or 22/7.... assuming I am trying to proof rationality of 22/7, what strictions can i include in my proof.

[@joaobrites5931]

What if you wanted to prove the other way around? Given that the sum of 2 numbers is rational, prove that they are both rationals.?

[@DrTrefor]

That statement (the converse) isn't actually true. pi + -pi=0 which is rational

[@joaobrites5931]

@@DrTrefor yes yes. i forgot a important part sorry. the question goes like this :if the sqrt(a) + sqrt(b) is rational, prove that sqrt(a) and sqrt(B) are rational. thank you.

[@vayramjosh]

is 2/1 a rational number ?

[@stargazer8718]

Despite having watched this many times, I still don't understand. Since it can't be more clear than this, how can I ever understand? Seems that my college degree is doomed to fail.

[@andescosmico3016]

Yes, it can be more clear if it would say: m+n=(p1.q2+p2.q1)/(q1. q2), but (a) the numerator (p1.q2+p2.q1) is an integer, let us call it p3, and (b) the denominator q1.q2 is also an integer let's call it q3, from (a) and (b) we get that m+n= p3/q3 where p3 and q3 are both integers, hence m+n is rational This proof is less formal than the one on the video, but it may be more clear.

[@emilyau8023]

@@andescosmico3016 your explanation was more clear. Thank you.

[@likethewordsmith]

Why we represent rational number as p/q (where p and q are integer and q not equal to zero).proof ?

[@RajdeepMehta]

Good to know that Indian are also watching 😂 👍🏻👌🏻

[@zzzzzzzjsjyue2175]

There is no proof. That’s the definition

[@ytseberle]

Nice video. But you keep saying q1q2 is the lcd of q1 and q2.

[@cringy7-year-old5]

pretty cool

[@stuartkent383]

My kids year 8 homework asked if the √20 is rational. If I was smart enough to understand this, then I might know. Oh well!

[@jackcastro7259]

very well explained . wishing to be smart as you hahahha

[@DrTrefor]

You are!

[@utopiad4]

Is 0.23 rational or irrational

[@andescosmico3016]

See my comment which is above yours.

[@fatmafaizal07]

wow