Den lördagen den 21:e december 2013 kl. 09:36:19 UTC+1 skrev Virgil: > In article <email@example.com>, > > firstname.lastname@example.org wrote: > > > > > > If WM claims the set of finite formulae is to be considered countable, > > let him prove it by listing its members. > > > > And if WM considers the set of real numbers to be countable, > > let him prove THAT by listing its members. > > > > Oh, that's right, Cantor twice proved otherwise. > > --
My very lose understanding of infinity, we can construct an algorithm that create an unfinite number terms in a list the simplest would be 1+1+1..., but we can not ever complete the list and never find the last member. Thus the last term creating a list of infinitly many members is incomplete and unreachable by deduction.
We can also find algoriths that add terms to an infinite list towards a limit using fractions, but also there we can never actually reach our limit we only work towards it infinitly. So even with our limit set we can not complete the list, that said the list representing the number do not really exist, it is a stipulation regarding something impossible you can not reach the limit even if you add terms infinitly. Because as soon as you reach add up terms that actually represent your limit, your sequense do not longer hold infinitly many terms/members. You can create the algorithm but the idea that it actually will reach the limit is simply not true.
An example her idea about adding clownes reaching the limit is simply a malformed mathematical statement, likewise the idea of 0.999... equal 1, 0.333... equal 1/3 is also either malformed or false statements.
Assigning a numerical magnitude to infinity is pure nonsense there exist no numerical magnitude that can represent such a number, any such magnitude is merely a limit proposed by the human mind.
So within my mind, this is also true for geometrical objects, the circle and curves is simply a stipulation about impossible geometric and numerical precision. There exist no such geometric object thats made up of an infinite number points/vertices. Mathematical/realworld objects using infinitly many members do not exist, sure you can go on claim their existence.
But in truth they are just dreamed up by the human mind without any form of justification.