# Operator: 'Greater Than Or Equal To' is not 'equasive' or 'inequasive' So what is it?

Lets say we use the following symbols for operators:

<    (less than)
<=   (less than or equal to)
>    (greater than)
>=   (greater than or equal to)
=    (equal to)
/=   (not equal to)


Now, extrapolating from wikipedia...

This type of operator is an equasive operator

=    (equal to)


These are inequasive operators:

<    (less than)
>    (greater than)
/=   (not equal to)


So what are these called?

<=   (less than or equal to)
>=   (greater than or equal to)


Any help appreciated.

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I've never heard these relations called "operators" before, nor heard equality called "equasive", nor inequalities called "inequasive". Are you inventing this terminology yourself? If so, it's up to you to extend it, not us. –  Chris Eagle May 9 '12 at 10:22
I'm using the terms 'operator' because I come to this question from a computer programming perspective see Relational_operator. I use the terms equasive/inequasive because I assumed that, say, the operator within 'inequation' would be 'inequasive'. –  JW01 May 9 '12 at 10:28
@JW01: We just call it a "relation", but this question isn't really about "relation algebra". –  Zhen Lin May 9 '12 at 10:35
Thanks for the hint. I tweaked the tag. –  JW01 May 9 '12 at 10:38

These relations (or the formulas in which they occur) are called (weak) inequalities. The term "inequality" (for the formula) is used in opposition to "equality" or "equation", not to indicate that they force their subexpressions to be different. So it is perfectly acceptable to say the inequality $x\leq y$ holds, even if it is in fact the case that $x=y$.
So, I guess going down the scale of quasivity we have; 'identicality', 'equality', 'weak inequality', 'strict inequality' and 'incomparability'. That's very helpful. Thanks. –  JW01 May 9 '12 at 11:51