Set Theory

Linear Algebra

These are topics learned in linear algebra (I took MATH 115) which is a course I took back in 1A.

A set is a collection of elements. For example, the set $X=\left\{2,4,7\right\}$ contains elements 2, 4, and 7.

$\varnothing$ is used to denote the empty set and $|S|$ denotes the size of a set.

You can do set operations like:

• Intersection
• Union
• Complement ($\bar{A}$ which depends on the universal set (elements of the universal set not in A))
• Difference

You can also take subsets, where is each element of $A$ belongs to set $S$, then $A$ is a subset of $S$. A set always has $2^{|s|}$ subsets which includes $\varnothing$.

Implementations of Set

In Java

• HashSet: Fast and unordered (uses .equals())
• TreeSet: Sorted set (uses .equals())
• LinkedHashSet: Ordered by insertion (uses .equals())
• IdentityHashSet: Unordered (uses ==)