#apache #archlinux #asterisk #centos #debian #gentoo #haskell #kde #kubuntu #lisp #math #mysql #perl #python #ruby-lang #rubyonrails #suse #ubuntu #vim #wikipedia 0 1 2 3 4 5 6 7 8 9 10
Top Prev 5368 5369 5370 5371 5372 5373 5374 5375 5376 5377 5378 5379 5380 5381 5382 5383 5384 5385 5386 Next
#math
<Olathe> Can you write each closed term in a finite number of characters ?
<futurist> yeah
<futurist> oh
<Olathe> Then it is a finite number in a computer.
<joblot> i suppose the numbering would be based on the parse tree
<futurist> but i have infintiely many characters
<joblot> but the parse is finite
<joblot> parse tree
<futurist> joblot i only half understand
<futurist> there are finite steps in construction sequence, yeah
<futurist> *finitely many
<Olathe> You have N^finite, which is not quite continuous.
<futurist> continuous?
<futurist> i don't need continuity..
<Olathe> Yes, as in uncountable.
<Olathe> N^finite can be represented with N by interleaving.
<futurist> hrm.. i only know continuity from analysis, not in this metalogic context
<JabberWalkie> ahhhh.....i must be getting sleepy....
<futurist> and i'm not sure what N^fintie means, we don't have that
<JabberWalkie> i approximated 1/(1+10^(-8)) as 1/10^(-8) :(
<Olathe> You have a vector of characters.
<Olathe> The vector is finite in size.
<Olathe> Thus, the bits can be interleaved.
<futurist> by vector of characters you mean the sequence that is the closed term?
<Olathe> Yes.
<futurist> the characters are the bits?
<Olathe> The characters are countable, so each is mapped to a natural.
<Olathe> Naturals can be written in binary.
<Olathe> You take the least significant bits of all the characters, then the next bit of each, then the next bit of each, and so on.
<Olathe> To form one natural.
<futurist> err wait, how do i know the characters are countable? i have countable constants, and then countable n-place functions for every n
<Olathe> Right. The constants are odd, the functions are even numbers.
<Olathe> Or however you want it.
<futurist> but how would i even list the functions?
<futurist> by zig zag i guess?
<Olathe> They're countable, so I assume that's doable.
<Olathe> You don't need to specify a method.
<futurist> well, for each n, i have countably many
<Olathe> What is n ?
<futurist> for each natural, i mean
<futurist> i have countably many 1-place functions, then countably many 2-place functions, etc.
<Olathe> OK, then you can do like this: arity, function_number, argument1, argument2, ...
<futurist> oh wait, i think i see--i'm thinking of the 'fixed stock' rather than the language itself
<futurist> i'm not sure that works--i tried it but you have infinite possible arguments
<Olathe> Not really.
<futurist> ? the language has infinitely many constants
<Olathe> Each function takes a finite number of arguments, right ?
<futurist> yeah
<Olathe> The constants each fill one argument.
<futurist> yeah so it's like an ordered pair from n
Previous Page Next Page