Quick maths question

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25 Jul 2003
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Whats the difference between (0,t) and (0,t] when expression a period of time? I tried google but you cant really search for ) ] !!

Cheers
 
In what context are we speaking of?
OMG!! i sound clever lol!! I have no idea what that means but oh well. All i will say is BLEH! That answers all inportant questions.
 
ripped from wiki does this help?

In mathematics

In addition to the use of parentheses to specify the order of operations, both parentheses and square brackets can also be used to denote an interval. The notation [a, c) is used to indicate a sequence from a to c that is inclusive of a but exclusive of c. That is, [5, 12) would be the set of all real numbers between 5 and 12, including 5 but except 12. The numbers may come as close as they like to 12, including 11.999 and so forth (with any finite number of 9s), but 12.0 is not included. In Europe, the notation [5,12[ is also used for this.

The endpoint adjoining the square bracket is known as closed, while the endpoint adjoining the parenthesis is known as open. If both types of brackets are the same, the entire interval may be referred to as closed or open as appropriate. Whenever infinity or negative infinity is used as an endpoint, it is always considered open and adjoined to a parenthesis.

This is used in mathematical notation, and appears in some computer programming languages. See the article Interval (mathematics) for a more complete treatment of the subject.

In quantum mechanics, angle brackets are also used as part of Dirac's formalism to note vectors from the dual spaces of the Bra 〈A| and the Ket |B〉. In statistical mechanics, angle brackets denote ensemble or time average.

In group theory and ring theory, square brackets are used to denote the commutator. In group theory, the commutator [g,h] is commonly defined as g−1h−1gh. In ring theory, the commutator [a,b] is defined as ab − ba. Furthermore, in ring theory, braces are used to denote the anticommutator where {a,b} is defined as ab + ba.
 
Lagz said:
Whats the difference between (0,t) and (0,t] when expression a period of time? I tried google but you cant really search for ) ] !!

Cheers


the difference between () and [] is inclusion.

(0,t) is the open set of all points 0<x<t

(0,t] is still an open set (I think), but it DOES contain the point t, ie
x: 0<x<=t


hth


edit: note to self: refresh tabs!
 
Amleto said:
(0,t] is still an open set (I think)...
It's neither open or closed. It's not open because each point in the neighbourhood of {t} is not in the set. It's not closed because a(n) = t/n is a sequence in (0,t] which converges to 0 which is not in the set.

In the same sense that there are lots of sets that aren't open or closed, there are some that are both open and closed.

:)
 
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