3 ms·
I’ve seen this used in the context of statements like “x is less than, equal to, or greater than y if and only if w is less than, equal to, or greater than z”.
by joppy 5y ago
I’ve seen this used in the context of statements like “x is less than, equal to, or greater than y if and only if w is less than, equal to, or greater than z”. Which might be written “x ⪋ y if and only if w ⪋ z”.
- wodenokoto 5y agoWhen is x not less than, equal to, nor greater than y ? Is it like, x is complex and y isn't?
- joppy 5y agoThe original text is meant to mean a triple of statements: x < y if and only if w < z x = y if and only if w = z x > y if and only if w > z This can be tiresome (and obviously confusing) if you need to keep using it in many places, hence some authors define the odd symbol to start with, and then use that in many places.
- gilrain 5y ago“If and only if” also has a shorthand in “iff”.
- SAI_Peregrinus 5y agoSurreal games[1] are probably my favorite example. But any partially-ordered set without total order can be an example. [1] https://en.wikipedia.org/wiki/Surreal_number#Games https://en.wikipedia.org/wiki/Surreal_number#Games