EECS20N: Signals and Systems

# 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.