Interval (mathematics) facts for kids
In mathematics, an interval is a group of numbers that includes all numbers between a starting point and an ending point. Think of it like a segment on a number line. Numbers that are bigger than the start and smaller than the end are inside the interval. Numbers outside this range are not part of it. The interesting part is that the starting and ending numbers themselves might or might not be included in the interval.
For example, an interval could be from 3.3 to 15. Numbers like 4, 8, 9.5, and 14 are inside this interval. Even 14.999 is in it! But numbers like -4, 2, 3.2, or 20 are not.
To write an interval, we use special symbols. You write either a square bracket ( [ ) or a parenthesis ( ( ), then the starting number, a comma ( , ), the ending number, and finally a closing square bracket ( ] ) or parenthesis ( ) ).
Here are some examples of how intervals look:
- (4, 9.6)
- [-100, 100]
- [-30, -4)
Contents
Different Kinds of Intervals
Intervals are named based on how they behave at their ends. They can be closed, open, or mixed.
Closed Intervals
A closed interval includes both its starting and ending numbers. It's like saying "from A to B, including A and B." We use square brackets ( [ and ] ) to show a closed interval.
For example, the interval [3, 5.4] includes the number 3, the number 5.4, and every number in between them. Another example is [136, 450].
Open Intervals
An open interval does not include its starting or ending numbers. It's like saying "from A to B, but not A or B." We use parentheses ( ( and ) ) to show an open interval.
For example, the interval (3, 5) includes all numbers between 3 and 5, but it does not include 3 or 5 themselves. Another example is (2, 5).
Mixed Intervals
A mixed interval is open at one end and closed at the other. This means it includes one of the end numbers but not the other.
- If it's written as [a, b), it includes 'a' but not 'b'. This is called a right-open interval.
- If it's written as (a, b], it includes 'b' but not 'a'. This is called a left-open interval.
For example, the interval [9, 23) includes the number 9, but it does not include the number 23.
Images for kids
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The addition x + a on the number line. All numbers greater than x and less than x + a fall within that open interval.
Related pages
See also
In Spanish: Intervalo (matemática) para niños
