h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

My dear Ariston,

Can zero play part in this set?



"Memory and imagination are the same, which for diverse reasons have diverse names."---Schwartzwald

Indeed, my friend. I haven't had the chance to elaborate more, but your point goes along with the third axiom and my commentary on it.

"In a way, the choice of the number 1 is an arbitrary one. It serves as a marker or starting point to begin in one direction."

So, if we like, we can begin the set with the number 0. But there is no reason why the choice of one number is better than the next. It depends on the frame of reference and applicability. If we were working with a set that began with the number 2, we would start there. The same can be said for the number -2.

The main idea behind these axioms is to formally develop what we take for granted as 'the counting numbers'.

Ariston

Oh yeah, I guess that I didn't give a reason why I chose the number 1 as a starting point.

Mainly because of the second axiom. The axiom describes the successor of any given number in the set. This is done by adding the number 1. So, by beginning with the number 1, the second axiom does not presume the existence of another number.

This way, the number 1 constitutes the entirety of all numbers in the set. If we began with the number 0, the second axiom would introduce a second number.

Ariston