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Sets for regular expressions - Coggle Diagram
Sets for regular expressions
Types of sets
Finite set : a set whose elements can be counted off by natural numbers up to a particular number
Cardinality: the number of elements in a finite set
Infinite set : a set which has no end value represented by "..." at the end of the set
Countable: a set which can be counted off against a subset of the natural numbers
Whether finite or infinite the important point to note here is that the individual elements of a countable set can always be counted off one at a time and although the counting may never finish every element of the set is associated with a unique natural number
countably infinite set a set where you can count the elements off against the set of natural numbers
Set comprehension
| = "such that"
E = "Belongs to"
^ = "and"
x = "cross" cartesian product of two sets is the set of ordered pairs eg A cross B = (a1,b1,a1,b2 etc)
Number type sets
.
natural numbers {N}: The set of positive counting numbers (1, 2, 3, ...)
Whole Numbers {W}: The set of natural numbers plus zero (0, 1, 2, 3, ...).
Integers {Z}: The set of whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3, ...)
.Rational Numbers {Q}: Any number that can be expressed as a fraction of two integers, such as (1/2), (-3/4), or (5) (which is (5/1)). This includes all integers, terminating decimals, and repeating decimals
.Irrational Numbers{Q}: Real numbers that cannot be expressed as a simple fraction, such as (\pi ) or (\sqrt{2})
.Real Numbers {R}: The set of all rational and irrational numbers, which represents all points on a number line
Complex Numbers {C}: Numbers that include an imaginary part, written in the form (a+bi), where (a) and (b) are real numbers and (i) is the square root of (-1).
Empty set {} , O a set containing no items