
Never equal
I just wonder what symbol you use for never equal. For example, $\displaystyle \equiv$ means that what is on the left side is always equal to what is on the right side. But what does $\displaystyle \not\equiv$ mean, does it men that what is on the left side is not always equal to what is on the right side, or does it mean that those are never equal? What symbol am I to write if I mean "never equal"?

Hi,
Err... This one ? $\displaystyle \neq$

As of your suggestion, $\displaystyle \neq$ simply means not equal, which could just be for a special case and not true for another case, hence what one can say is just that they are not always equal. Never equal means that the condition $\displaystyle \neq$ would be true for every possible combination of values for the different variables affecting the expression.
Then, does $\displaystyle \not\equiv$ men not always equal or never equal?

Maple 11 (a Math's program) calls the ≢ symbol "nequiv".
I don't know what it stands for, probably "never equivalent"..?

Well, if you want to satisfy certain conditions, you could use $\displaystyle \ne$ in combination with $\displaystyle \forall$ which means for all. Once again, you could define what is happening (i.e. your conditions) in English or whatever language you choose. However, we all speak one language here  Mathematics.