Much of mathematics involves reasoning about relationships between things.  For example, high school algebra is very concerned with when two things are the equal (i.e. the same).  Set theory cares a lot about whether a given element is a member of a given set, or whether a given set is contained in another.

Relationships in this sense are so fundamental to everyday language that they're almost difficult to talk about.  A relationship between two kinds of things either holds (is true) of a given pair of things, or doesn't hold (is false).  For example, ownership holds between me and my car (I own it), but not between me and your car (I don't own it).

In mathematics, we usually notate that a relationship \(R\) holds between two objects \(a\) and \(b\) by writing: \(aRb\).  You've already seen this with many different relationships:

• \(a=b\)
• \(a<b\)
• \(a\in b\)
• \(a \subset b\)
• etc.

But we could equally well do it for less “mathy” relationships:

• \(a \text{ owns } b\)
• \(a \text{ is the mother of }b\)
• \(a \text{ is older than }b\)
• \(a \text{ likes }b\)
• \(a \text{ voted for }b\)
• \(a \text{ is an organ of }b\)
• \(a \text{ can fix }b\)
• \(a \text{ is a cure for }b\)

Although, given math's love of single-character names for things, we might well find the mother relation notated \(aMb\) rather than \(a\text{ is the mother of }b\).