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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 wo
by MrManatee 5y ago
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.
- School-Cotton 5y agoIf you wanted to avoid this in math notation without being overly verbose you could write x,y \in (0,1) and x <= y.
- MrManatee 5y agoYeah, 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 https://en.wikipedia.org/wiki/Minkowski_inequality