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Number sets - Sets of numbers

Natural numbers : N 
Whole numbers : \(N_0\)
Integers : Z
Positive integers : \(Z^+\)
Negative integers : \(Z^-\)
Rational numbers : Q
Real numbers : R
Complex numbers : C

  1. Natural Numbers 
    Counting numbers : N= {1,2,3,...} .
  2. Whole Numbers 
    Counting number and zero : \(N_0= \{0,1,2,3,...\}.\)
  3. Integers
    Whole number and their opposites and zero : 
    \(Z^+=N= \{1,2,3,...\},\)
    \(Z^-=N= \{...,-3,-2,-1\},\)
    \(Z=Z^- \cup \{0\} \cup Z^+=\{...,-3,-2,-1,0,1,2,3,...\}.\)
  4. Rational Numbers
    Repeating or terminating decimals 
    \(Q=\bigg \{ x|x= {a \over b }\;\; and \;\;a\in Z \;\; and \;\; b \in Z \;\; and \;\; b\ne 0 |\bigg \}\)
  5. Irrational Numbers 
    Nonrepeating and nonterminating decimals 
  6. Real Numbers 
    Union of rational and irrational numbers : R. 
  7. Complex Numbers 
    \(C = \{x+iy |x \in R \;\; and \; \; y \in R \},\)
    Where i is the imaginary unit.
  8. \(N \subset Z \subset Q \subset R \subset C\)