Learning outcomes

After studying this course, you should be able to:

• find a rational and an irrational number between any two distinct real numbers

• solve inequalities by rearranging into simpler equivalent forms and solve inequalities involving modulus signs

• state and use the Triangle Inequality and use the Binomial Theorem and mathematical induction to prove inequalities which involve an integer n

• use the strategies introduced for determining least upper bounds and greatest lower bounds

• explain how the least upper bound property is used to define arithmetical operations with real numbers and explain the meaning of rational powers.