Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Why is the fundamental theorem of arithmetic special?

  1. Dec 30, 2014 #1
    Why is it significant enough to be fundamental?

    Some people say that it is fundamental because it establishes the importance of primes as the building blocks of positive integers, but I could just as easily 'build up' the positive integers just by simply iterating +1's starting from 0.
     
  2. jcsd
  3. Dec 30, 2014 #2

    FactChecker

    User Avatar
    Science Advisor
    Gold Member

    Yes, you can build up all natural numbers by adding 1's. The primes do the same thing from the point of view of multiplication as 1 does from the point of view of addition. If you want to build up all the natural numbers using multiplication, you need to use primes.
     
  4. Dec 30, 2014 #3
    In that case, why is multiplication so special? What makes it more special than addition, exponentiation, tetration, pentation, hexation, ... ?
     
  5. Dec 30, 2014 #4

    FactChecker

    User Avatar
    Science Advisor
    Gold Member

    Multiplication is certainly not more "fundamental" than addition, but building up the natural numbers by adding 1's is apparently not difficult enough to call it a theorem. It may be how the natural numbers are defined. Multiplication and addition are the fundamental operations that are used to define the other operations.
     
  6. Dec 30, 2014 #5

    MarneMath

    User Avatar
    Education Advisor

    If the question has to due with the fact why it has the name it has. I imagine this is a tradition bestowed upon it by the fact that the theorem has existed since Euclid. I'm sure there may exist other reasons. Anyway, I wouldn't get to hung up on the name. Sometimes we just name things so everyone knows what we're talking about.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Why is the fundamental theorem of arithmetic special?
  1. Fundamental Theorems (Replies: 3)

Loading...