# Introduction to analysis

This free course is an introduction to analysis, which looks at real numbers and their properties, with a particular emphasis on inequalities.

# Learning outcomes

- 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.