Below is a list of sets whose sizes we are interested in comparing.

The original list:

$\mathbb{Z}$, the set of all integers.

$\mathbb{N}$, the set of positive integers (also called "natural numbers").

$\mathcal{P}(\mathbb{N})$, the power set of $\mathbb{N}$.

$\mathbb{R}$, the set of all real numbers (points on a number line).

[0,1], the closed interval from 0 to 1, defined as {x : x is a real number and 0 $\leq$ x $\leq$ 1}.

$\mathbb{Q}$, the set of all rational numbers

$\mathbb{C}$, the set of all complex numbers

Added in class, 3-8-10

(0,1), the open interval from 0 to 1, defined as {x : x is a real number and 0 < x < 1}.

Added by Dr. Ksir, 3-9-10

$I_n$, the integers from 1 to n.

$(1, \infty)$, aka {x : x is a real number and 1 < x }.

Added in class, 3-10-10

The set of even positive integers.

The set of nonnegative integers, $\mathbb{N} \cup \{0\}$.

$\mathcal{P}(I_n)$, the power set of $I_n$.

{x : x is an integer and x > 5}