Of course we are not being asked for the truth-value of the statement here, only the meaning implied by the syntax.

As to whether x ‘is less than’ y can be taken to mean the same as y ‘is greater than’ x is indeed a moot point. Of course it does, but we haven’t been told so.

I agree, the exercise is sloppy. I suggest you write to the webmaster and point this out.

]]>What we are discussing here is First Order Logic (FOL) and although it is a formal deductive system used in linguistics and philosophy it is interpreted by mathematical structures. Herein lies the problem of trying to take the maths out of logic. You’ve taken the red pill because talking about seemingly simple stuff in a generalised fashion means getting very deep.

My set (group and field too) theory is rather rusty having graduated in 1999 but I’m just getting a feel again for why I did maths in the first place. You have a healthy non-acceptance of non-rigorous statements which means I’m going to have to root out some proper definitions. Browsing wikipedia has revealed the need to discuss propositional functions, indicator functions, relations, axioms and then your on to really fundamental questions about existence, consistency and completeness.

I really want to make the time to at least come up with an intuitive proof. I think a formal one is out of the question. So I’ll have to get back to you on this as I must first repose your question in a mathematical way.

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