Sequence

A sequence is an (often infinite) ordered collection in which repeats are allowed. Alternatively, a sequence $(𝑎 𝑛) \infty 𝑛 = 1$ may be thought of as a function $𝑓 : ℕ \to {𝑎 𝑛} : 𝑛 \mapsto 𝑎 𝑛$ . If $𝑓$ is a bijection, the sequence induces a Totally ordered set of ${𝑎 𝑛}$ with an initial object. Similarly, any countable set can be given a total order by a bijective sequence. By skipping some terms of a sequence one gets a Subsequence.

Properties

convergent sequence ⇒ Cauchy sequence ⇒ bounded sequence

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