[globular-toast]

I was also a bit confused by this. I thought the standard notation was round brackets, but maybe doesn't work well in ASCII?

[qbit42]

Round brackets are standard in the US but that notation is used in France and some other places.

[meindnoch]

  (0, 1)

Is this an twice-open interval or a 2D vector?

See, this is why Bourbaki introduced the ]0,1[ notation.

[streetfighter64]

Is there any reasonable situation where you'd be confusing a vector with an interval? Having done mathematical writing and grading of tests using both styles of notation (simply adapting to what was used at the institution), I can't say that I ever noticed any practical difference between them.