Unique Factorization Theorem

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Learn the proof of how every number can only be represented in a unique way from prime factorization!
  1. JustAGuyWhoLikesMath
  2. unique
  3. prime
  4. prime factorization
  5. factorization
  6. unique factorization theorem
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Комментарии
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Thanks prof, could you please continue and expand your repertoire because you are a gifted educator. Thanks again.

sharifahmed
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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.

paulmatthewduffy
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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.

RohitVishwakarma-btcx
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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.

fullfungo
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the more generalized proof should consider the number of p's and q's to be not equal.. Cheers for this excellent proof though

mohammedalimuddin
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Isn't this called *The Fundamental theorem of Arithmetic* ?

TechToppers
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I do not understand why p has to divide qi (just before 3 minute mark)

hadee.guitarist