Number

An element of a Division Ring, used for measuring, counting, quantifying, etc.

Set Name	Symbol	Description	Examples
Natural Number	$\mathbb{N}$	Counting numbers	$1,2,3,42$
Whole Number	$\mathbb{W}$ or ${\mathbb{N}}_0$	Nonzero Integers	$0,1,2,3,42$
Integer	$\mathbb{Z}$	Natural numbers, their negatives, and zero.	$-5,0,12$
Rational Number	$\mathbb{Q}$	Any number expressible as a fraction $\frac{p}{q}$.	$0.75,\frac{1}{3},-4$
Irrational Number	${\mathbb{Q}}^{\prime }$	Numbers that cannot be fractions (non-repeating decimals).	$\pi ,e,\sqrt{2}$
Real Number	$\mathbb{R}$	All points on the continuous number line ($\mathbb{Q}\cup {\mathbb{Q}}^{\prime }$).	$1.5,\pi ,-22$
Imaginary Number	$\mathbb{I}$	$\mathbb{R}\cdot i$	$1.5i,\pi i,-22i$
Complex Number	$\mathbb{C}$	$a+bi,a,b\in \mathbb{R}$	$2+3i,5,-i$
Quaternion	$\mathbb{H}$	$a+bi+cj+dk,a,b,c,d\in \mathbb{R}$	$1+5i+2j+3k$
Octonion	$\mathbb{O}$	$a+bi+cj+dk+el$ + fm+gn+ho$$a,b,c,d,e,f,g,h \in \mathbb{R}	Takes up too much space