[MrManatee]

How about relation chaining, such as with inequalities? Is there some nice S-expression notation for, say, "0 < x ≤ y < 1"? In many programming languages you would have to write "0 < x and x <= y and y < 1", but in mathematics this kind of repetition would quickly become very cumbersome.

[umanwizard]

If you wanted to avoid this in math notation without being overly verbose you could write x,y \in (0,1) and x <= y.

[MrManatee]

Yeah, I suppose this would be acceptable in this instance. But it still repeats x and y, and if x and y were complicated expressions instead of just simple variables, I wouldn't want to repeat them.

For example, the proof of the Minkowski inequality in Wikipedia [1] contains a statement of the form "x_1 = x_2 = x_3 ≤ x_4 = x_5 ≤ x_6 = x_7". Except that x_1, ..., x_7 are so complicated that any notation that requires repeating them doesn't feel like a satisfactory notation for "all of mathematics".

[1] https://en.wikipedia.org/wiki/Minkowski_inequality