from The Open University
Alternatively you can skip the navigation by pressing 'Enter'.
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.
Other pages You might like
Explore: Learning about numbers
Sue Johnston-Wilder looks at how we develop our skills with numbers
Try: Grad, Div and Curl
Have you ever wondered what causes cyclones, and why it's always calm in the centre of...
Try: Egyptian mathematics
The Egyptians are known for being ahead of their time in comparison to some civilisations...
Study: The story of maths
This short course traces the development of mathematics – from its origins in Egypt and...
Explore: Lab Rats: Sperm diary
Read Mike Leahy and Zeron Gibson's sperm diary, as part of the BBC/OU's programme website...
Try: The Fourier Series
Fourier analysis encompasses a vast spectrum of mathematics which is often deemed...
Try: Achieving public dialogue
There are a wide range of interactions between ‘science’ and ‘the public’....
Study: Pure mathematics
This Level 2 course - for those with prior mathematical knowledge - introduces the main...
Explore: Chinese at the tip of your tongue:...
Just like in other cultures, numbers have hidden meanings in Chinese culture too....
Try: Rollercoaster design
Why is a rollercoaster so exciting and terrifying, yet safe? Modern rollercoasters such...
Try: Symmetry
We all encounter symmetry in our everyday lives, in both natural and man-made structures....
Study: Postgraduate Diploma in Mathematics
This postgraduate diploma is ideal for mathematicians, mathematically inclined scientists...
Comments
Be the first to post a comment
Copyright & revisions
Copyright information
- 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.
Feeds
If you enjoyed this, why not follow a feed to find out when we have new things like it? Choose an RSS feed from the list below. (Don't know what to do with RSS feeds?)
Remember, you can also make your own, personal feed by combining tags from around OpenLearn.
Alternative Formats
Tags, Ratings and Social Bookmarking
About this site
Views
Votes
Comments
Tags
- climate change (373)
- business (277)
- diaries (194)
- bottom line (169)
- food (168)
- Rough Science (162)
- BBC Two (145)
- internet (145)
- BBC Radio 4 (140)
- BBC (133)
- Scotland (121)
- points for debate (120)
- listings (120)
- Bang goes the Theory (116)
- children (116)
- Creative Climate (116)
- English Civil War (115)
- astronomy (108)
- Thinking Allowed (104)
- religion (98)
- marketing (94)
- 20th century (94)
- Charles I (93)
- communication (92)
- evolution (91)
- sustainability (89)
- research (88)
- architecture (85)
- energy (83)
- Charles Darwin (78)
OpenLearn Links
