My topology teacher appears to call a monoid a set with an associative binary operation, but with no identity element. According to wiki, this is the definition of a semi-group, although they remark that some authors define semi-groups as having an identity (i.e. synonymously to monoid). But they don't say on the monoid article that some authors take monoid to mean an associative magma(groupoid) with no identity.(adsbygoogle = window.adsbygoogle || []).push({});

So, does my teacher simply has the definitions mixed up or do some authors effectively call 'monoid' an associative magma(groupoid)?

I wanted to ask here before throwing the "Sir professor, according to wikipedia, you're wrong" at him. I'm sure that's understandable.

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# Semi-groups and monoids

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