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.
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.
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.
@@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.
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!!
Glad it helped!
You are an excellent teacher!
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.
I go to ucla, paid something around 1k for this class to be confused, your video might be the thing that saves me.
Almost halfway through the discrete math course, Thank you very much for these videos.
Thank you so much,your lectures saved me👏👏👌
You have saved a soul
Well done sir
Tq you sir you solved my problem
I watch these videos and then go to the book "Introduction to Algorithms" or CLRS and see how much more I understand.
Wow amazing to listen from you
or 22/7.... assuming I am trying to proof rationality of 22/7, what strictions can i include in my proof.
is 2/1 a rational number ?
Why we represent rational number as p/q (where p and q are integer and q not equal to zero).proof ?
Good to know that Indian are also watching 😂 👍🏻👌🏻
There is no proof. That’s the definition
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.
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.
@@andescosmico3016 your explanation was more clear. Thank you.
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.?
That statement (the converse) isn't actually true. pi + -pi=0 which is rational
@@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.
pretty cool
Nice video. But you keep saying q1q2 is the lcd of q1 and q2.
very well explained . wishing to be smart as you hahahha
You are!
Is 0.23 rational or irrational
See my comment which is above yours.
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!
wow