- Infinite Set
A set with uncountable number of elements is said to be an infinite set. In other
words, if the cardinal number of a set could not be found then the set is said to be an
infinite set.
Eg. : C = {1, 2, 3, ...}
Provide the child with a bowl full of sand grains and ask him/her to count the grains.
Counting the grains is practically impossible, and now explain the concept of an
infinite set, orally.
Note : In other words, a set which is empty or consists of a definite number of
elements is called finite, other wise the set is infinite.
For example,
Set of days of the week
Set of vowels in the English alphabet
A = { x| 1≤x≤10, x∈^ N}
B = { x| 15>x, x N} are all finite sets, while
N – Set of natural numbers
Z – Set of integers
Q – Set of all rational numbers
C = { x|x>11, x∈N}
the set of points in a line, etc., are all infinite sets.
- The Null Set / The Empty Set / The Void Set
A set with no elements is said to be the null set or the empty set or the void set.
Eg. : B = {Horses with six legs}
C = { x| x+8 = 4, x∈N}
D = { x| x+4 = 4, x N}