Sets:Definitions

Definitions

A set is any collection of objects. The objects in a set are called elements. For example, $\mathbb {N} ={1,2,3,....}$ is the set of all natural numbers, and any positive integer is an element of this set. Sets do not necessarily have to contain mathematical elements. For example, we can say $P=$ {"red", "orange", "yellow", "green", "blue", "indigo", "violet"} is a set that contains the standard rainbow colors as its elements. To denote that an element $x$ is in a set $S$, we write $x\in S$. This is read as "$x$ is an element of $S$". If $x$ is NOT in the set $S$, we write $x\not \in S$. For example, looking at our set of colors $P$, we can see that "green" $\in P$ and "grey" $\not \in P$. If we consider the set of natural numbers, $5\in \mathbb {N}$, while $-7.5\not \in \mathbb {N}$.

Resources

• Course Textbook, pages 93-100