Salutator comments on A Pure Math Argument for Total Utilitarianism - Less Wrong

-5 Post author: Xodarap 27 October 2013 05:05PM

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Comment author: Salutator 04 November 2013 10:30:52PM 0 points [-]

I'm a bit out of my depth here. I understood an "ordered group" as a group with an order on its elements. That clearly can be finite. If it's more than that the question would be why we should assume whatever further axioms characterize it.

Comment author: Xodarap 19 January 2014 12:56:25PM 0 points [-]

If it's more than that the question would be why we should assume whatever further axioms characterize it

from wikipedia:

a partially ordered group is a group (G,+) equipped with a partial order "≤" that is translation-invariant; in other words, "≤" has the property that, for all a, b, and g in G, if a ≤ b then a+g ≤ b+g and g+a ≤ g+b

So if a > 0, a+a > a etc. which results means the group has to be torsion free.

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