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msg908
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Joined: July 26th, 2005, 3:50 am

Length of half closed intervals

June 8th, 2006, 7:06 am

Hi,why is it that the length of half-closed intervals such as [a,b) = b-a ?Thank youmsg
Last edited by msg908 on June 7th, 2006, 10:00 pm, edited 1 time in total.
 
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zarnywhoop
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Joined: December 2nd, 2004, 5:39 pm

Length of half closed intervals

June 8th, 2006, 7:38 am

What do you think it should be? I'm not sure I understand the source of confusion. Intuitively, the length of [a,b) is clearly greater than [a,c] for any c < b, and less than that of [a,c] for any c > b.Does this help?
 
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TGN
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Joined: December 14th, 2003, 6:02 pm

Length of half closed intervals

June 8th, 2006, 6:40 pm

We have [a,b] = [a,b) + [b,b]. Rearranging we get (assuming the Lebesgue measure): [a,b) = [a,b] - [b,b] = b-a - (b-b) = b-a.
 
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doreilly
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Joined: February 1st, 2005, 1:22 am

Length of half closed intervals

June 8th, 2006, 7:04 pm

b is measure zero
 
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msg908
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Length of half closed intervals

June 9th, 2006, 12:40 am

Thanks guys.msg