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JoshuaZ comments on Stupid Questions Open Thread Round 2 - Less Wrong Discussion

15 Post author: OpenThreadGuy 20 April 2012 07:38PM

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Comment author: Incorrect 20 April 2012 11:13:55PM * 1 point [-]

Is this a correct statement of what a well-ordering of R is?

$\exists A (\text{total-order}(A, \mathbb{R}) \land \forall B (B \subseteq \mathbb{R} \land B \neq \emptyset \implies \exists x \in B \forall y \in B ((x \preceq y) \in A))) \forall A \forall B (\text{total-order}(A, B) \iff \forall a \forall b \forall c(a, b, c \in B \implies (((a \preceq b) \in A \lor (b \preceq a) \in A) \land ((a \preceq b) \in A \land (b \preceq a) \in A \implies a = b) \land ((a \preceq b) \in A \land (b \preceq c) \in A \implies (a \preceq c) \in A))))$

Comment author: gjm 21 April 2012 12:06:00AM -1 points [-]

Looks OK to me, though I can't guarantee that there isn't a subtle oops I haven't spotted. (Of course it assumes you've got some definition for what sort of a thing (a <= b) is; you might e.g. use a Kuratowski ordered pair {{a},{a,b}} or something.)

JoshuaZ comments on Stupid Questions Open Thread Round 2 - Less Wrong Discussion

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