Length of half closed intervals

msg908 · 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

zarnywhoop · 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?

TGN · 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.

doreilly · June 8th, 2006, 7:04 pm

b is measure zero

msg908 · June 9th, 2006, 12:40 am

Thanks guys.msg