Conclusion

Following completion of this free OpenLearn course, Introduction to analysis, as well as being able to ‘understand some of the basic elements of analysis’ you should also find that your skills in producing convincing arguments and problem solving are improving.

You should now 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.

This free OpenLearn course is an extract from the Open University course M208 Pure mathematics [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .

If you feel you are ready to move on in your study of pure mathematics but don’t have time to study a full Open University course at this time, you might like to study one of the free OpenLearn courses Introduction to group theory or Introduction to linear equations and matrices. They are further adapted extracts from the Open University course M208 Pure mathematics.

Alternatively, if you are interested in applied mathematics, you might like to try the free OpenLearn courses Second-order differential equations and Dynamics. If you are interested in statistics, you might like to try the free OpenLearn courses Modelling and estimation, Medical statistics, and Bayesian statistics.