The Fundamental Theorem of Arithmetic is easy enough to understand, saying that every integer greater than 1 is either prime or is the product of a unique combination of prime numbers.
What I don't understand is why this is "fundamental." This may have massively important implications in number theory and cryptography and whatever else, but in terms of arithmetic, which I think of as adding, subtracting, multiplying, and dividing, it doesn't really actually seem to have that much importance....I don't see why it should be so fundamental.
Can someone explain its importance, or why it isn't called perhaps the "Fundamental Theorem of Number Theory"?
I would expect the Fundamental Theorem of Arithmetic to be something.