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### Learning Math: A Blank Is A Blank With A Blank

Recently, I found myself in the curious position of trying to learn something again. Funny how that keeps happening. I’m trying to understand something called a “Galois connection,” and a kindly stranger on the Internet recommended a text called “The Galois Connection between Syntax and Semantics” by Peter Smith.

I found it online, started reading, and found this definition of a “partially ordered set” or “poset,” which is one of those annoying prerequisites for understanding what a “Galois connection” is. Here’s the explanation:

``````A partially ordered set - henceforth, a poset - is a set P, carrying an
ordering relation which is reflexive, anti-symmetric and transitive.
``````

Okay, this seems simple enough but there are definitely some more prerequisites here - “ordering relation,” “reflexive,” “anti-symmetric,” and “transitive.” Where to go from here?

This post isn’t at all about what a Galois connection or a Poset is. Instead it’s about the shape of the definition above, a shape that is common enough that you see it everywhere, from math texts to computer science texts, programming language manuals, etc. I like to call it:

# A Blank Is A Blank With A Blank

This kind of question comes up a lot with programmers who are trying to learn some more theory: