# (x,x] = {x}

by rukawakaede
Tags: None
P: 2,490
 Quote by tiny-tim why should it? the interval (3,2] doesn't contain 2, so why should (2,2] ? yes, elements "strictly greater than x and less than or equal to x" don't include x
I'm sorry. Why do you say that (3,2] doesn't include 2? As a half closed interval doesn't this notation correspond to $$3> x \geq 2$$? Please explain why you are saying 2 is not included in the interval when every reference I've checked says it is. I'll just post one.

http://mathworld.wolfram.com/Half-ClosedInterval.html
 PF Patron Sci Advisor Emeritus P: 8,837 No, (3,2] is the set of all real numbers x such that 3
P: 2,490
 Quote by Fredrik No, (3,2] is the set of all real numbers x such that 3
OK. But that's not the inequality I wrote in my previous posts. However for (a,b] I do see your point. If I write $$a < x \leq b$$ then the corresponding set has no least element and therefore cannot be well ordered. Thanks.