On Apr 9, 10:38 pm, apoorv <skj...@gmail.com> wrote: > 'There is , at least such a thing as "relative unaccountability" . > You can't enumerate the contents of an infinite integer list : > 1 , 0 , 1 , 0 , 1 ...... > > 'There's always the "...." left out . > However , you can unambiguously describe the infinite list by finite > wording : > > "an integer on the list has : > Value 1 if it's on an 'even position on the list' . > Value 0 if it's on an 'odd position on the list' . > > This finite description unambiguously captures my 'infinite list' . ' > > This finite description uses the universal quantifier, which > Allows a finite string of symbols to convey an infinite amount > Of information.Is that a realistic assumption? > Apoorv
If I make a program that gives for each number n as input the output 1- (n%2) , I can be reasonably sure it's the desired sequence . The information is finite. You've got it backwards . We can use a finite amount of information to generate an infinite string . You could say we're never interested in the structure of the infinite string per se (in the sense that we never directly observe the infinite string in its entirety ), rather , in the structure and morphology of the different 'shapes of information' that describe the string .
Anyway, there are different 'shades' of mathematics along the line between 'finitism' and 'platonic realism'. What I said is only not realistic for some extreme forms of finitism . It works from 'effective computability' upwards.