https://stau.space/tags/mathematics/Recent content in Mathematics on stau.spaceHugoen-USsona@stau.space (Sona Tau Estrada Rivera)sona@stau.space (Sona Tau Estrada Rivera)Fri, 17 Jul 2026 20:34:54 -0400https://stau.space/posts/perfect-structure/Tue, 16 Jun 2026 11:48:48 -0400sona@stau.space (Sona Tau Estrada Rivera)https://stau.space/posts/perfect-structure/<p>An <a href="https://en.wikipedia.org/wiki/Algebraic_structure">algebraic structure</a> is a set with some functions associated to it that meet some axioms. <a href="https://en.wikipedia.org/wiki/Semigroup">Semi-groups</a>, <a href="https://en.wikipedia.org/wiki/Field_%28mathematics%29">fields</a>, <a href="https://en.wikipedia.org/wiki/Quasigroup">loops</a>, and <a href="https://en.wikipedia.org/wiki/Magma_%28algebra%29">magmas</a> are all examples of algebraic structures. I won&rsquo;t assume that the reader has dealt with any of these structures but I will assume that you know about <a href="https://en.wikipedia.org/wiki/Cardinality">set cardinality</a> and the fact that these structures were originally created, mostly, in an abstract way in order to model different things. The best example for this, from a programming perspective, is that of the semigroup. If you want to parallelize a procedure in your program, a way to do this would be to demonstrate it forms a semigroup. If so, parallelizing it is super easy, since a semigroup&rsquo;s operation is associative. I won&rsquo;t go into too much detail on this since this is not the point of this post.</p>