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:

k

a

n

K


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.

If the infimum is a term in the sequence it is called the minimum.

If the supremum is a term in the sequence it is called the maximum.

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