4 ms·
>But there are uncountably many finite collections of symbols How do you mean? Because there are uncountably many symbols? I'm not really sure what a symbol me
by sebzim4500 4y ago
>But there are uncountably many finite collections of symbols
How do you mean? Because there are uncountably many symbols? I'm not really sure what a symbol means in this context.
- auggierose 4y agoI just picked on one of the points in the post that make no sense without further explanation. Just take each real number as a symbol.
- davrosthedalek 4y agoIt's normally assumed that the number of symbols is finite.
- ceceron 4y agoThe number of symbols in the language may countable, but the number of sets of symbols will be indeed uncountable, i.e. AFAIR the number of sets of natural numbers is uncountable — you can even construct real numbers as sets on rational (still countable) numbers.
- deleted 4y ago[deleted]
- drdeca 4y agoThe set of all sets of natural numbers is uncountable, but the set of all finite sets of natural numbers, is countable.
- ceceron 4y agoTrue, that's why I haven't used 'finite' in my comment. Apparently I've missed that the parent referred to the finite collections and in fact was wrong making my previous comment misplaced. Thanks for pointing it out :)