Talk:Interval (mathematics)

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Doesn't the definition of Interval make as much sense for a poset as a totally ordered set? There is a link to this page from poset that would suggest as much. I'll make the change and expect someone to let me know if I am way off base. ;-> -- Jeff 18:20 Jan 22, 2003 (UTC)

Ah, just changing the definition to use posets allows incomparable elements to be an "Interval" which just wouldn't be right. So I guess the reference from poset is really pointing to the interval notation which can be extended to posets (and just might produce empty sets a lot). Is this used enough to be worth mentioning? -- Jeff

I added [a,b] for a partially ordered set - Patrick 23:00 Jan 22, 2003 (UTC)

In the section about Interval Arithmetic... Division by an interval containing zero is indeed possible if some extensions are made. This makes it possible to get answers such as .

Divsion with intervals may result in two intervals. Ex. say [1,1]/[-1,1] results in two intervals. [-inf,-1] and [1,inf]

Contents 1 Varying vs. constant interval 2 fixed improper examples of open and closed intervals 3 Types 4 Interval Arithmetic in Fortran and C++

[edit] Varying vs. constant interval

Let's say P₁ = Q₁ = 100 and P₅ = Q₅ = 500, but P₂ = 197, P₃ = 301 and P₄ = 404, while Q₂ = 200, Q₃ = 300 and Q₄ = 400——i.e., the "P" and "Q" endpoints are the same, while the "Q"s are equally spaced between each other, and the "P"s aren't. For example (TN = "term number" and UT = upper TN):

while

Would the proper definition/identification be "the Q's provide auxiliary points between P₁ and P₅ at a constant interval"? Or does this concept have an established name? This article doesn't appear to address this variation.  ~Kaimbridge~20:01, 16 February 2006 (UTC)

[edit] fixed improper examples of open and closed intervals

The reason I'm making a change: There are many things wrong with the text I am replacing, but mostly it's because by definition an interval is a set which contains two endpoints so a single valued set can not be an interval. The previous definitions for open and closed intervals also looks more like a discussion of numbers dating back to the turn of the previous millennia where scholars where discussing odd and even numbers more as a philosophical problem. Open and closed intervals have nothing to do with single valued sets nor whether [integers] are open or closed.

Reference: "Calculus With Analytic Geometry" by Earl W. Swokowski, Prindle, Weber & Schmidt, 1979, ISBN: 0-87150-268-2. Pages 5 and 6.

I've removed the following: Intervals of type (1), (5), (7), (9) and (11) are called open intervals (because they are open sets) and intervals (2), (6), (8), (9), (10) and (11) closed intervals (because they are closed sets). Intervals (3) and (4) are sometimes called half-closed (or, not surprisingly, half-open) intervals. Notice that intervals (9) and (11) are both open and closed, which is not the same thing as being half-open and half-closed.

Intervals (1), (2), (3), (4), (10) and (11) are called bounded intervals and intervals (5), (6), (7), (8) and (9) unbounded intervals. Interval (10) is also known as a singleton.

The length of the bounded intervals (1), (2), (3), (4) is b-a in each case. The total length of a sequence of intervals is the sum of the lengths of the intervals. No allowance is made for the intersection of the intervals. For instance, the total length of the sequence {(1,2),(1.5,2.5)} is 1+1=2, despite the fact that the union of the sequence is an interval of length 1.5.

and added the following: Intervals using the round brackets ( or ) as in the general interval (a,b) or specific examples (-1,3) and (2,4) are called open intervals and the endpoints are not included in the set. Intervals using the square brackets [ or ] as in the general interval [a,b] or specific examples [-1,3] and [2,4] are called closed intervals and the endpoints are included in the set. Intervals using both square and round brackets [ and ) or ( and ] as in the general intervals (a,b] and [a,b) or specific examples [-1,3) and (2,4] are called half-closed intervals or half-open intervals.

Rockn-Roll

[edit] Types

In the section "Higher mathematics," intervals that are closed at infinity should be mentioned as well. (e.g. the extended reals.)

[edit] Interval Arithmetic in Fortran and C++

Should it be noted that the Sun Studio compilers implement Interval Arithmetic? --rchrd 03:13, 11 July 2006 (UTC)