# What is the definition of binary sequence?

Can I write an infinite binary sequence like so: ...0111001001, ...10010

because I saw some people write infinite binary set from left to right like so: 1011000... , 101111...

But I was not sure if the oposite works also,

because I am not so familiar with binary sequence definition and I can't find any answer for this anywhere in the internet. Thank you in advance.

• Sure you can. Context should tell you whether a given situation calls for a finite string or not. – lulu Apr 15 '16 at 14:00
• It's just informal notation. You can write them either way. – Thomas Andrews Apr 15 '16 at 14:09

You can think of a binary sequence as a map from the natural numbers, $\mathbb N,$ to the set of values $\{0,1\}$.
Whether you express those maps, informally, as "$f(0),f(1),f(2),\dots$" or "$\dots,f(2),f(1),f(0)$" is essentially irrelevant, unless you want to mix the two notations and give them different meanings. Then you'd have to take some care about what you mean by the notation.
$$\dots010111101\dots$$
Those are intrinsically different, and correspond to maps from $\mathbb Z$ to $\{0,1\}$, possibly modulo some equivalence relationship, or you'd want your notation to somehow indicate which element corresponds to $0\in\mathbb Z$.