Some Basic Sets

Naturals	=	{1,2,3, ... }	natural numbers
Naturals ₀	=	{0,1,2,3, ... }	non-negative integers
Integers	=	{ ... , -3,-2,-1,0,1,2,3, ... }	integers
Integers₊	=	{0,1,2,3, ... }	non-negative integers, same as Naturals ₀
Reals	=	(- ∞, ∞)	real numbers
Reals₊	=	[0, ∞)	non-negative real numbers
Complex	=	{x + jy \| x ∈ Reals, y ∈ Reals}	complex numbers
Chars	=	{a, ... , x, A, ... , X, ... }	set of all alphanumeric characters
Char*	=	{a, ... , x, aa, ab, ... , ax, ... }	set of all finite character strings
Binary	=	{0, 1}	binary values
Binary*	=	{0, 1, 00, 01, ... }	set of all finite binary strings

The notation (-∞, ∞) refers to the (continuous) range of real numbers from minus infinity to plus infinity. In general (a, b) refers to a range from a to b, without including either a or b in the set. To include a and b in the set, we use square brackets, as in [a, b]. The square brackets may be mixed with parentheses, so for example, [0, ∞ ) refers to the range of real numbers from zero (inclusive) to infinity, without including infinity.

Sets representing physical quantities

Time	=	(a, b)	a span of time, from a to b.
Pressure	=	Reals₊	air pressure
Temperature	=	(-273.15, &infi;)	temperature (in Centigrade)
Intensity	=	Reals₊	brightness of light

These sets are usually ordered sets with the usual numerical ordering relation. This allows us to compare two time values, for example, to say that one time is earlier (less than, "<") another.