NotesByLex

Special Infinite Set

Lex Toumbourou ·

Some special infinite sets come up all the time in math:

  • Z\mathbf{Z} = set of integers = {...,2,−1,0,1,2,...}\{...,2,-1,0,1,2, ...\}
  • N\mathbb{N} = Z+\mathbf{Z^{+}} = set of positive integers = {1,2,3,...}\{1,2,3,...\}
  • Z−\mathbf{Z-} = set of negative integers = {...,−3,−2,−1}\{. . . , -3, -2, -1\}
  • W\mathbf{W} = set of whole numbers = {0,1,2,3,...}\{0,1,2,3,...\}
  • Q\mathbf{Q} = set of rational numbers = {p/q∣p,q∈Z∧q≠0}\{p/q|p, q ∈ \mathbf{Z} ∧ q \neq 0\}
  • R\mathbb{R} = set of real numbers
  • R+\mathbb{R^{+}} = set of positive real numbers = {x∈R∣x>0}\{x ∈ R|x > 0\}
  • R−\mathbb{R}- = set of negative real numbers = {x∈R∣x<0}\{x ∈ R|x < 0\}

They can be very useful to memorise.