1.1 Comparisons of Monoid Elements

s = t
s < t

The equality operator = evaluates to true if the monoid elements s and t are equal and to false otherwise. The inequality operator < evaluates to true if the monoid elements s and t are not equal and to false otherwise.

You can compare monoid elements with objects of other types. Of course they are never equal. Standard monoid elements are transformations (see Binary Relations).

s < t
s <= t
s = t
s t

The operators <, <=, = and evaluate to true if the monoid element s is strictly less than, less than or equal to, greater than or equal to and strictly greater than the monoid element t. There is no general ordering on monoid elements.

Standard monoid elements may be compared with objects of other types while generic monoid elements may disallow such a comparison.

  
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