[seqfan] Gauss bracket vs Iverson bracket (was: A024812).

[Peter Luschny]

> Personally I like the Gauss brackets to denote the floor function
> (as part of my lost-in-advance battle in favour of traditional
> notation vs computer/programming language induced "deformations")

I applaud to your intention which I support. On the other hand in
the case of the floor function I disagree.

The symbol [.] was split up by Iverson to [.] with the upper angles
removed to denote the floor function and the lower angles removed
to denote the ceiling function. A natural and intuitive extension
of the Gauss bracket.

But as this cannot be represented by the usual 'typewriter notation'
(though it could be typed in the past using some ball-head typewriters)
writing floor() and ceiling() seems appropriate to me.

Moreover, this move sets the symbol [.] free for other meanings.
Iverson (and Knuth) suggest the following meaning:

   [b] = 1 if the b is true and 0 otherwise.

Good use of this notation can often simplify formulas considerably
and make clumsy two dimensional case differentiations, as often seen
in mathematical texts, dispensable.

Peter