
Re: ?? 524 Are finite cardinal numbers natural numbers?
Posted:
Jul 21, 2014 3:24 PM


On Thursday, July 17, 2014 1:11:32 PM UTC5, FredJeffries wrote: > Why does is matter a fetid dingo's kidney?
When the original question is phrased appropriate, then the answer to your question also becomes immediately apparent.
The correct phrasing of the question is: are natural numbers and finite ordinals the same as far as those using them are concerned? (i.e. are they used interchangeably?)
The answer is most definitely not and that's unfortunate, because it leads to a significant degeneration and (over)complication in the math and technical literature; not the least being in the countless places where people use indexing from 1 (instead of 0) and then write their sum operators as (Sigma_{n = 1}^{n = P} instead of Sigma_{n in P}). That's just the beginning. It cascades from there, leading to inefficiency on top of inefficiency.
Almost all papers (and programs) I read, process, review and use I end up first rewriting. And the failure to make effective use of natural numbers as cardinals is one of the many points of leakage that turn what could be easily, concisely stated into a NASA project. So, as a result, most of what I end up processing gets reduced by about 50% or more, even *with* an increase in content. That applies to mathematical proofs, text and programs.

