2005 Student Research Conference:
18th Annual Student Research Conference

Mathematics and Computer Science

Rearrangements of Almost Convergent Sequences
Christopher C. Bay
Dr. Eric Howard, Faculty Mentor

An infinite sequence of numbers (x1, x2, x3, . . .) is said to converge to the number x if every interval (a,b) around x, no matter how small, contains all but a finite number of terms of the sequence. The number x is called the limit of the sequence, and the idea of a limit can be generalized in a way that assigns a limit to every bounded sequence. The generalized limit of some sequences can depend on arbitrary choices, but for others it is unique. Such sequences are called almost convergent. What happens when the terms of an almost convergent sequence are rearranged? Any rearrangement of a convergent sequence will also converge, but the same is not true for almost convergent sequences. The question of when almost convergence is preserved by a rearrangement is a very interesting one. This question will be addressed, and many examples will be given to illustrate the character of these unusual sequences.

Keywords: sequences, limit, almost convergence, rearrangements, infinite series

Topic(s):Mathematics

Presentation Type: Oral Paper

Session: 8-3
Location: VH 1408
Time: 8:45

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