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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.

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

You could also have sequences that go in both directions:

$$\dots010111101\dots$$

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 $0\in\mathbb Z$.

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  • $\begingroup$ Such a "sequence" that "goes in both directions" is often called a bisequence. $\endgroup$ – murray Feb 5 at 19:32

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