I am sad because my attempt to teach you about preference reversals has almost certainly failed.

ADDED. For reference, here is the whole dialog on preference reversals.

ADDED. On most subjects, I would have let my esteemed interlocutor have the last word so as to keep the peace and so as not to appear as a self-aggrandizing jerk who cannot stop trying to get one up on the person I am disagreeing with. I humbly suggest however that in subjects like math where there often is an objectively-correct fact of the matter, everyone benefits a lot from writers not being too afraid to be confrontational. One of those benefits is "clarity" (something concrete for the reader's mind to latch onto), something easily lost in the abstractions in conversations about math. In other words, I humbly suggest that a competent writer involved in a dialog about math will appear to observers who are not used to good dialogs about math to be unnecessarily domineering, rude, dogmatic or otherwise socially inept even if he is not.

ADDED. In other words, in internet discussions on math (or programming languages), if you care too much about not insulting or embarrassing your interlocutor, my experience has been that the whole discussion tends to become a hazy fog.

ADDED. I am open to learning from others here how to improve the social side of my communications in dialogs like this.