Why is the fundamental theorem of arithmetic special?

  • Thread starter japplepie
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  • #1
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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.
 

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  • #2
FactChecker
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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.
 
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In that case, why is multiplication so special? What makes it more special than addition, exponentiation, tetration, pentation, hexation, ... ?
 
  • #4
FactChecker
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In that case, why is multiplication so special? What makes it more special than addition, exponentiation, tetration, pentation, hexation, ... ?
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.
 
  • #5
MarneMath
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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.
 

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