BOUNDED SEQUENCES | |
Analysis | |
6. DEFINITION OF A BOUNDED SEQUENCE | ||||||||
A sequence is said to be boundedif it has an upper boundand a lower bound. |
||||||||
13.- Note that in this sequence: 7 is an upper boundand -2is a lower bound and therefore, when represented on the Cartesian plane, the points in the sequence are found between the lines y=7and y=-2. 14.- Check that the same thing happens for any other upper or lower bound Kand k, i.e. the points in the sequence are between the lines y=Kand y=k. In other words, for any term n:
|
||||||||
7. INFIMUM AND SUPREMUM | ||
The greatest lower bound is known as the infimumand the least upper bound as the supremum. |
||
15.- Find the supremumand infimumof the sequence in this window.
16.- Check that the sequence in the window has a maximum, as the supremum forms part of the sequence, but it does not have a minimumas the infimum does not form part of the sequence. |
||
Juan Madrigal Muga | |
Spanish Ministry of Education and Education. Year 2002 | |