It's important to separate the structure from the objects. There's 2-the-natural-number, 2-the-integer, 2-the-rational, and 2-the-real. In each context, it's

It's important to separate the structure from the objects. There's 2-the-natural-number, 2-the-integer, 2-the-rational, and 2-the-real. In each context, it's the "same" 2, but the structure we put around it is different. The structure is what makes it interesting. 2-the-rational is not prime. There are no primes when every non-zero element has a multiplicative inverse. An element with a multiplicative inverse is called a unit and for the same reason we exclude 1 from being prime we exclude units from being primes in other structures. Every non-zero real number is a unit. Every non-zero rational is a unit. Only -1 and 1 are units in the integers. Only 1 is a unit in the naturals.