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.
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.
Thanks prof, could you please continue and expand your repertoire because you are a gifted educator. Thanks again.
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.
100th subscriber! :)
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.
This is Amazing :)
This is helpful, thank you
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
@Muhammad Ashraf what do you mean by “1
Great proof thanks a lot :)
the more generalized proof should consider the number of p's and q's to be not equal.. Cheers for this excellent proof though
Isn't this called *The Fundamental theorem of Arithmetic* ?
Yeah lol
awesome work
That's helpful...🙂🙂
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.