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In our everyday lives we use we use language to develop ideas and to communicate them to other people. In this free course, Mathematical language, we examine ways in which language is adapted to express mathematical ideas.
After studying this course, you should be able to:
- use set notation
- determine whether two given sets are equal and whether one given set is a subset of another
- find the union, intersection and difference of two given sets
- determine the image of a given function
- determine whether a given function is one-one and/or onto.
Study this free course
Enrol to access the full course, get recognition for the skills you learn, track your progress and on completion gain a statement of participation to demonstrate your learning to others. Make your learning visible!
When we try to use ordinary language to explore mathematics, the words involved may not have a precise meaning, or may have more than one meaning. Many words have meanings that evolve as people adapt their understanding of them to accord with new experiences and new ideas. At any given time, one person's interpretation of language may differ from another person's interpretation, and this can lead to misunderstandings and confusion.
In mathematics we try to avoid these difficulties by expressing our thoughts in terms of well-defined mathematical objects. These objects can be anything from numbers and geometrical shapes to more complicated objects, usually constructed from numbers, points and functions. We discuss these objects using precise language which should be interpreted in the same way by everyone. In this course we introduce the basic mathematical language needed to express a range of mathematical concepts.
Please note that this course is presented through a series of downloadable PDF files.
This OpenLearn course is an adapted extract from the Open Unviersity course
Copyright & revisions
Originally published: Tuesday, 28th June 2011
Last updated on: Monday, 22nd February 2016
- 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 and our FAQs section.
- This site has Copy Reuse Tracking enabled - see our FAQs for more information.
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All our alternative formats are free for you to download, for more information about the different formats we offer please see our FAQs. The most frequently used are Word (for accessibility), PDF (for print) and ePub and Kindle to download to eReaders*.
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- PDF (3.2 MB)
- ePub 3.0 (1.3 MB)
- ePub 2.0 (1.3 MB)
- Kindle (201 KB)
- RSS (30 KB)
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- OUXML Package (7 KB)
- OUXML File (17 KB)
- IMS Common cartridge
*Please note you will need an ePub and Mobi reader for these formats.