What Is a Sequence? - Real Numbers and Limits in Mathematics

Explore the mathematical concept of sequences in this 27-minute lecture from the Insights into Mathematics series. Delve into the precise definition of sequences, starting with finite sequences of natural numbers. Learn to distinguish between sequence specification and description, and understand how large sequences can exhibit qualitatively different properties. Examine various types of sequences, including those of natural numbers, primes, and rational numbers. Discover valuable resources like N. Sloane's On-line Encyclopedia of Integer Sequences. Gain a deeper understanding of this fundamental mathematical concept through clear explanations and examples.

Intro to sequences
Sequences of natural numbers
Definition of a sequence
Specification of a sequence
Truly specified sequences
Sequence of primes
Sequences of rational numbers