root `fundamental theorem of arithmetic` Notes
Fundamental Theorem of Arithmetic see psi function, monoid > fold theorem every nonzero natural can be written as the product of a unique multiset of primes --- me example \(1200 = 2^4 3^1 5^2 = \times \{2, 2, 2, 2, 3, 5, 5\}\) note \(1 = \times \{\}\). stating that \(1\) has no prime factorization or excluding \(1\) from the fundamental theorem of arithmetic is a pedagogical sleight of hand. see https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic, https://math.stackexchange.com/questions/1549939/fundamental-theorem-of-arithmetic-why-greater-than-1, https://math.stackexchange.com/questions/47156/prime-factorization-of-1, https://youtu.be/IQofiPqhJ_s?t=251
© 2025 Emilien Breton `Notes/Notes/notes/fundamental theorem of arithmetic.md`

Fundamental Theorem of Arithmetic

theorem every nonzero natural can be written as the product of a unique multiset of primes --- me

example \(1200 = 2^4 3^1 5^2 = \times \{2, 2, 2, 2, 3, 5, 5\}\)

note \(1 = \times \{\}\). stating that \(1\) has no prime factorization or excluding \(1\) from the fundamental theorem of arithmetic is a pedagogical sleight of hand. see https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic, https://math.stackexchange.com/questions/1549939/fundamental-theorem-of-arithmetic-why-greater-than-1, https://math.stackexchange.com/questions/47156/prime-factorization-of-1, https://youtu.be/IQofiPqhJ_s?t=251