Real numbers

• All of calculus, and a lesser extent of linear algebra is about real numbers.
• We write real numbers in base 10, but this is a bit unnatural

Definition: the set of real numbers is the set of infinite decimals, preceded by a plus or minus sign

• A number ending in all 9’s is equal to a number ending in all 0’s
  • ex.
  • Also,
• For , we will denote as the number with all of the digits of to the left of the decimal, and exactly digits after.
  • Given two identical decimal constructions, will be the one with zeros.
• Given any two different numbers and , one is always bigger than the other