# “Set Membership” Symbol Redesign

## Set Theory

In high school and college math courses, we learn about ways to express groups of items as subsets and supersets. This branch of mathematics is called set theory.

The expression,

X ∈ A

means “Item X exists in set A”, or “X is an element of set A”. The symbol looks like an E, which is a helpful mnemonic, but it doesn’t visually convey its meaning very well. I thought it should be redesigned, so I stepped up to the task, and it appears my answer may be good enough, and not conflict with any existing symbol. The dot in my symbol represents an item being enveloped by a set or classification, while the C represents an enveloping group. The open end on the right gives the symbol a sense of imbalance, implying a sense of directionality between the terms on its left and right. The terms cannot be interchanged, due to the symbol lacking the property of commutativity.

Set theory is a powerful tool, and it is becoming more important for every-day computer science. It is used to describe things that need to be processed via list-comprehensions in functional languages as well as other languages.

I have written at length on the topic in my blog post: Set Theory in Programming.