I came across this in a Hacker News discussion. It’s a rigorous derivation of (positive) real numbers without using 0 or negative numbers at all. In other words, pretend that you don’t know what 0 and negative numbers are, come up with a slightly different axiom set for what is essentially a positive part of an ordered field, etc.
Interestingly, this isn’t stated as an explicit goal in the article, you need to read it between the lines.
The paper is weak evidence of what I was talking about in this thread; weak because actual aliens probably wouldn’t discover real numbers this way. But it does show it’s possible to quite easily talk and reason about them w/o ever employing negative numbers, or even 0.
http://arxiv.org/pdf/1303.6576
I came across this in a Hacker News discussion. It’s a rigorous derivation of (positive) real numbers without using 0 or negative numbers at all. In other words, pretend that you don’t know what 0 and negative numbers are, come up with a slightly different axiom set for what is essentially a positive part of an ordered field, etc.
Interestingly, this isn’t stated as an explicit goal in the article, you need to read it between the lines.
The paper is weak evidence of what I was talking about in this thread; weak because actual aliens probably wouldn’t discover real numbers this way. But it does show it’s possible to quite easily talk and reason about them w/o ever employing negative numbers, or even 0.