How does Cantor's diagonal argument work with bi-infinite sequences?

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I understand the basic premise of the argument when considering a list of infinitely long binary sequences; you arrange them in any order, take the inverse of items along a diagonal, and the sequence formed cannot be in the list.

I'm confused on how you can apply this to a bi-infinite sequence, that is, an infinitely long sequence that has no 'first' element, where any selected bit has infinitely many bits before and after it. Can anyone clear this up for me?