At lunch at Nuffield I was just asking MM about some math notation I’d like: a symbol for “is not necessarily equal to”. For example, and economics paper might show the following:

Proposition: Stocks with equal risks might or might not have the same returns. In the model’s notation, x IS NOT NECESSARILY EQUAL TO y.

I can’t say x \neq y there, because maybe x=y, maybe not, depending on the parameter values.

If anybody knows of such a symbol, please let me know. In fact, just a symbol for IS NOT NECESSARILY might be useful, since we could combine it with other symbols, e.g.

x IS NOT NECESSARILY = y

Horse heights ARE NOT NECESSARILY > cow heights

The biased estimator IS NOT NECESSARILY \sim N(0,1).

OCTOBER 7. Stimulated by a comment below:
The modal logic symbols might work well. Wikipedia’s “Modal logic” says:

“The basic modal operators are usually written (or L) for Necessarily and (or M) for Possibly.”

Maybe I could say ” x ≠ y” for “x is not necessarily equal to y”.

ztipypBUT (wrt 7/10) modal operators traditionally take propositions as their arguments; they are not relation-modifiers. This surely fits more closely with the original query? The original concern is with the status of an ‘a=b’ claim, not the thought that ‘a’ and ‘b’ are in some new, undefined, relation?? Further a new ‘a ? b’ relation remains undefined until we specify its entailments. [Propositional modal logic does provide a structure of entailments – – and plenty of (possibly relevant) fretting about the consistency of meaning of ‘necessary’ ]

You could use in conjunction standard modal logic operators (square for ‘it is necessarily the case that’, diamond for ‘it is possibly the case that’)?

?

ztipypBUT (wrt 7/10) modal operators traditionally take

propositionsas their arguments; they arenotrelation-modifiers. This surely fits more closely with the original query? The original concern is with the status of an ‘a=b’ claim, not the thought that ‘a’ and ‘b’ are in some new, undefined, relation??Further a new ‘a ? b’ relation remains undefined until we specify its entailments. [

]Propositionalmodal logic does provide a structure of entailments – – and plenty of (possibly relevant) fretting about the consistency of meaning of ‘necessary’You could use in conjunction standard modal logic operators (square for ‘it is necessarily the case that’, diamond for ‘it is possibly the case that’)?

KIM

Couldn’t you just stack <>=? This is available in Sci Workplace.