I am reading this. It says that a quasigroup is a magma in which division is always possible. I'm a little confuse with the meaning of division. Does division means that the inverse operation of $\bullet$ is always defined? I am thinking about the analogy in multiplication of integers, in which division is the inverse operation of multiplication. I guess divison implies that there are inverses.
2026-02-22 23:10:58.1771801858
What is the meaning of division for quasigroups in here?
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Since quasigroups are sometimes called division groupoids or
(this latter from the Wikipedia page you referenced), a bit of confusion may arise.
I suggest not to confuse division with division and cancellation and to read the proper definition of both in this article.