1.2 Types Of Sets

Empty Set - The Set With Nothing

A set containing no elements at all.

Symbols: $\phi$ or $\{ \}$

Number of elements: $n(\phi) = 0$

Important: $\phi \neq \{0\}$

$\phi$ has zero elements.

$\{0\}$ has one element (the number zero).

Don't confuse them!

Finite Sets - Countable

A set where you can count all elements and the counting ends.

Definition: A set with a definite number of elements.

Notation: $n(A)$ = number of elements in set $A$

When Are Two Sets Equal?

Two sets are equal if they have exactly the same elements.

Nothing more, nothing less.

Symbol: $A = B$

Key Point: Order doesn't matter. Repetition doesn't matter.

Only the elements themselves matter.