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(x,x] = {x}

by rukawakaede
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SW VandeCarr
#19
Mar20-11, 04:02 PM
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Quote Quote by tiny-tim View Post
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 [tex]3> x \geq 2[/tex]? 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
Fredrik
#20
Mar20-11, 04:18 PM
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No, (3,2] is the set of all real numbers x such that 3<x≤2. There are no such real numbers. Therefore, (3,2]=∅.
SW VandeCarr
#21
Mar20-11, 04:55 PM
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Quote Quote by Fredrik View Post
No, (3,2] is the set of all real numbers x such that 3<x≤2. There are no such real numbers. Therefore, (3,2]=∅.
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 [tex]a < x \leq b[/tex] then the corresponding set has no least element and therefore cannot be well ordered. Thanks.


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