Subsets of the Set R of Real Numbers
Subsets of the set R of real numbers
Following sets are important subsets of the set R of all real numbers:
(i) The set of all natural numbers N = { 1, 2, 3, 4, 5, 6,…. }
(u) The set of all integers Z = { … – 3, – 2, -1, 0,1, 2, 3,… }
(iii) The set of all rational numbers Q
if { x : x = m/n , m, n ∈ Z, n ≠ 0 }
(iv) The set of all irrational numbers. It is denoted by T.
Thus, T = { x:x ∈ R and x ∉ Q } .
Clearly, N ⊂ Z ⊂ Q ⊂ R,T ⊂ R and N ⊄ T.