Is Writing a Semi Group?

Question

While writing this question, I compose letters from a set $L=\{a,...z,A,...Z\}\cup\{\;\text{ } \;\}$. Writing has a binary operation which is associative. The result always is an element of $L^n$. Does this mean that Writing is a semi group?

Answer 1

The answer is yes, but as Rahul pointed out it's even a monoid. From the Wikipagepage:

In other words, a monoid is a semigroup with an identity element. It can also be thought of as a magma with associativity and identity.

I also found this nice figure:

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