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Numbers
Featuring: This unit will help you understand more about real numbers and their...
This unit will help you understand more about real numbers and their properties. It will explain the relationship between real numbers and recurring decimals, explain irrational numbers and discuss inequalities. The unit will help you to use the Triangle Inequality, the Binomial Theorem and the Least Upper Bound Property.
By the end of this unit you should be able to:
- explain the relationship between rational numbers and recurring decimals;
- explain the term irrational number and describe how such a number can be represented on a number line;
- find a rational and an irrational number between any two distinct real numbers;
- solve inequalities by rearranging them into simpler equivalent forms;
- solve inequalities involving modulus signs;
- state and use the Triangle Inequality;
- use the Binomial Theorem and mathematical induction to prove inequalities which involve an integer n;
- explain the terms bounded above, bounded below and bounded;
- use the strategies for determining least upper bounds and greatest lower bounds;
- state the Least Upper Bound Property and the Greatest Lower Bound Property;
- explain how the Least Upper Bound Property is used to define arithmetical operations with real numbers;
- explain the meaning of rational powers.
- Duration: 20 hours
- Published on: Wednesday 29th June 2011
- Level: Intermediate
- Posted under: Mathematics
Numbers
Introduction
This unit is devoted to the real numbers and their properties. In particular, we discuss inequalities, which play a crucial role in analysis.
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- Creative-Commons: The Open University is proud to release this free course under a Creative Commons licence. However, any third-party materials featured within it are used with permission and are not ours to give away. These materials are not subject to the Creative Commons licence. See terms and conditions. Full details can be found in the Acknowledgements section.
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