Defining intervals

### 6.6.1 Defining intervals

An interval is a range of real numbers, whose end points will be floats with at least 15 significant digits. The i command creates intervals, with the arguments in square brackets.

- i takes two arguments: a and b, two real numbers.
- i[a,b] returns the interval between a and b.

  If a > b, then i[a,b] returns i[evalf(b,15)-epsilon,evalf(a,15)+epsilon] (see Section 2.5.7, item 2.5.7).

Intervals can also be created by following a decimal number with a question mark. If the decimal number contains n digits, the interval will be centered at a and have width 2· 10−n.

#### Examples

i[1,13/11]

[1.00000000000000..1.18181818181819] |  |  |  |  |  |  |  |  |  |

i[pi,sqrt(3)]

[1.73205080756886..3.14159265358980] |  |  |  |  |  |  |  |  |  |

0.123?

| ⎡ ⎣ | 0.121999999999999..0.124000000000000 | ⎤ ⎦

789.123456?

| ⎡ ⎣ | 0.789123454999990e3..0.789123456999998e3 | ⎤ ⎦