Subsets

Definition

A subset is a set that is solely contained in another set. We say, "$\mathbb{X}$ is a subset of $\mathbb{Y}$" if every element of $\mathbb{X}$ is also an element of $\mathbb{Y}$

Formally:

In class I believe you will use "$\subseteq$" to denote a subset where the subset can equal the reference set and "$\subset$" to denote strict subsets - subsets that are not equal to the reference set.

Example

The Natural numbers (counting numbers starting from 0 or 1) are a subset of the integers. That is, every single natural number is contained within the integers.

Formally: $\mathbb{N} \subseteq \mathbb{Z}$

Since $\mathbb{N} \neq \mathbb{Z}$, we have: $\mathbb{N} \subset \mathbb{Z}$ or that the natural numbers are a strict subset of the integers.

Notes

Check Notation for clarification on what these symbols mean