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Interval

Usage

Interval[ min, max ]表示在minmax之间的值的范围。
Interval[  ,   ,   ,   , ... ]表示范围   ,   , .... 的并。


Notes

• 可以在对象Interval上进行算术和其他运算。
• 例如: Interval[ 1, 6 ] + Interval[ 0, 2 ]LongRightArrow .
Min[interval]Max[interval] 给出一个区间的端点。 • 对近似机器数或任意精度的数x, Interval[x]产生一个反映 x 的不确定性的一个区间。 • 在对涉及近似数的区间进行运算时,Mathematica总是四舍五入将下限向下上限向上。
Interval 可以由如同 Limit的函数产生。
• 如同EqualLess的关系运算,无论什么时候它们被给在不相交区间,就产生TrueFalse结果.
• 参见 Mathematica 全书: 3.6.8.
• 同时参见: Range.
Further Examples

You can use Max and Min to find the endpoints of intervals.

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You can take the union and intersection of the two or more intervals.

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Using IntervalMemberQ, you can check if an interval is contained in another.

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You can also check if a point belongs to an interval.

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You can do interval arithmetic with many functions. For example, this command reflects the fact that the square of any real number between -2 and 5 lies between 0 and 25.

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Taking the reciprocal gives two distinct intervals.

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You can use intervals in many kinds of functions.

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Some functions automatically generate intervals.

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With ordinary machine-precision arithmetic, this gives an incorrect result.

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The interval generated here, however, correctly includes the point 0.

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Interval arithmetic is useful in obtaining or proving bounds. Here we define a function  , which depends on two parameters  . We then show that this function is monotonically nonincreasing in  for all values of the parameter.

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