Sequence: Definition

Another discrete structure we'll talk about in this topic is a sequence.

A sequence is an ordered collection of various sorts of objects, which we call terms or sometimes coordinates, but the names items or elements are also proper. Examples:

• $(1, 2, 3)$ or $\langle1, 2, 3\rangle$ [

  $\langle 1, 2, 3\rangle$

  ]
• $(1, 2, 3, 4, \dots)$ or $\langle1, 2, 3, 4, \dots\rangle$
• $(\text{Alice},\,$$\text{Carol},\,$$\text{Eugene},\,$$\text{George})$ or $\langle\text{Alice},\,$$\text{Carol},\,$$\text{Eugene},\,$$\text{George}\rangle$
• $($😀$,$ 😁$,$ 😎$,$ 😜$)$ or $\langle$😀$,$ 😁$,$ 😎$,$ 😜$\rangle$

Unlike sets, since sequences are ordered, changing the order or repeating a term creates a whole new sequence:

$\langle😀,\,$$😁, \,$$😎\rangle \neq\;$$\langle😀, \,$$😎, \,$$😁, \,$$😎, \,$$😀, \,$$😀, \,$$😀\rangle.$

We will get back to sequences at the end of this topic. Let's get back to sets now.