= 27d567bc2d48d9f40e9ccc20ea370b15)
AnotherKevin comments on Gödel and Bayes: quick question - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (36)
Either I am confused or this discussion is confused.
N(X) iff (X=0) || ((X > 0) && N(X-1)) iff X is natural or 0
Z(X) iff ( (X >= 0) -> N(X) ) && ( (X < 0) -> N(0 - X) ) iff X is an integer
equivalently
I'm also under the impression that the algebraic numbers are countable, dense in R, and that
(\exists%20x((x%20\in%20\mathbb%20R%20)%20\vee%20P(x))%20\iff%20\exists%20y%20((\text{y%20is%20algebraic})%20\vee%20P(y))%0A)
Edit: note to all, mixing latex and plain text on a line looks messy. Further edited for formatting due to lack of preview.
If you're attempting to define N as a first order predicate, that doesn't work; you've defined it in terms of itself. You can't directly define predicates recursively; predicates must be finite. If you want to do get a "recursive" predicate you have to do quite a bit more work than that, and in particular you need tools not available in the first order theory of the reals (with addition and multiplication, as usual).
Your definition of Z has additional minor problems; you mean and, not implies. (X>=0 => N(X)) is automatically satisfied for any X<0.
Your last statement is correct (if a bit less general than it could be :) ), though your notation is a bit strange. (Again, assuming + and * as usual.)
Might I ask what the relevance of all this is?
Z is defined correctly. When X >= 0 the formula becomes N(X) AND TRUE when X < 0 the formula becomes TRUE AND N(0-X).
Otherwise I was confused. I was trying to define N implicitly which I should have recognized as invalid. Explaining what I was trying to say at the end would be pointless given that I didn't say it and it's also wrong =P. Mea culpa
Oh, you said "and"; my apologies, I implicitly read an "or" there!