Section outline

  • This section introduces the foundational structure of the real numbers as a complete ordered field.

    Content:

    • Field axioms (addition and multiplication properties)

    • Order axioms (trichotomy law, transitivity, etc.)

    • The interaction between algebraic and order structures

    • The absolute value function and its properties

    • Intervals: open, closed, half-open, bounded/unbounded

    Learning Outcomes:

    • Understand and apply the axioms of a field and an ordered set

    • Use inequalities and algebraic manipulation within ℝ

    • Interpret and construct subsets of ℝ using interval notation