I'm just saying to get to 1 through multiplication you can always multiply any number by its own inverse (which is another way of saying divide any number by itself)
I.e. X * 1/X = X/X = 1, always.
I guess, technically, it's a division needed to get the inverse, so it's perhaps it doesn't count :-)
Edit: Ah, yeah, now with help from the reply below I see my mistake - you're saying the inverse itself cannot exist since we're only dealing with natural numbers, that makes sense.
I guess that's pretty much the reason that only multiplication in allowed in the OP's original question, allowing division lets us get all kinds of fractional numbers which wouldn't be allowed.
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.
