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Signed-off-by: Jim Pryor <profjim@jimpryor.net>
A **monoid** is a structure `(S, *, z)` consisting of an associative binary operation `*` over some set `S`, which is closed under `*`, and which contains an identity element `z` for `*`. That is:
A **monoid** is a structure `(S, *, z)` consisting of an associative binary operation `*` over some set `S`, which is closed under `*`, and which contains an identity element `z` for `*`. That is:
-<blockquote>
-for all `s1`, `s2`, `s3` in `S`:<BR>
-(i) `s1*s2` etc are also in `S`<BR>
-(ii) `(s1*s2)*s3` = `s1*(s2*s3)`<BR>
+<pre>
+for all `s1`, `s2`, `s3` in `S`:
+(i) `s1*s2` etc are also in `S`
+(ii) `(s1*s2)*s3` = `s1*(s2*s3)`
(iii) `z*s1` = `s1` = `s1*z`
(iii) `z*s1` = `s1` = `s1*z`
Some examples of monoids are:
Some examples of monoids are: