Available online
Description
This programme deals with the convergence of sequences of numbers.
This programme deals with the convergence of sequences of numbers.
| Module code and title: | M203, Introduction to pure mathematics |
|---|---|
| Item code: | M203; 30 |
| First transmission date: | 1980 |
| Published: | 1980 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:23:37 |
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| Producer: | Jack Koumi |
| Contributors: | Timothy R. Lister; Peter Strain-Clark |
| Publisher: | BBC Open University |
| Keyword(s): | Asymptotic; Continuity; Domain Inverted; Function; Nested Intervals |
| Footage description: | The programme develops a reformulation, in terms of continuity, of the definition for convergence of a sequence of numbers. The reformulation is used to develop rules which generate new convergent sequences. The definition for convergence of a sequence of numbers involves the convergence of a sequence of nested intervals. The programme starts by relating this definition to the idea of getting closer and closer (to a, number c) as we go further and further (along the sequence of numbers). The second part of the programme identifies a sequence of numbers as a function from the integers to the reals and relates this idea to that of an asymptotic function from the reals to the reals. The definition of asymptotic is then reformulated in terms of continuity of a "domain-inverted" function. This leads to a reformulation of the definition of convergence in terms of the continuity of a restricted domain-inverted function. The final part of the programme uses the reformulated definition to derive rules for combining convergent sequences to produce new ones. The rules are directly analogous to the familiar rules for combining continuous functions. |
| Master spool number: | HOU3258 |
| Production number: | FOUM064X |
| Videofinder number: | 4108 |
| Available to public: | no |
