Interval notation in algebra.?

Question

Can someone explain interval notation in easy to understand language? Thanks

Answer 1

Brackets [ and ] mean closed interval, i.e. including the endpoint.
Parentheses ( and ) mean open interval, i.e. excluding the endpoint.

Thus:
"2 <= x < 5" is equivalent to "x in [2,5)"
"-1 < y <= 3" is equivalent to "y in (-1,3]"

Answer 2

Like everybody else said, round brackets mean exclusive and square brackets mean inclusive.

If x is in the interval (4,6), then that means
4 < x < 6

If x is in the interval [4,6), then that means
4 <= x < 6 {that symbol means "less than or equal to" but isn't typed out that way}

You can guess then what (4,6] and [4,6] mean.

What you will also encounter with interval notation is the concept of infinity. For instance, x > 4 can be interpreted as
x in the interval (4, infinity). The key thing to remember about infinity and -infinity is that they are ALWAYS round brackets.

Lastly, you'll encounter the U symbol, for union.

If I wanted to interpret the statement x >= 4 or x < -8, then we would write it in interval notation as follows:

[4, infinity) U (-infinity, -8)

Note that the interval ALWAYS contains the smaller number first and then the bigger number. [8, -2) would not be valid for interval notation.

Answer 3

Intervals first of all are just every number between the two numbers given. What is sometimes confusing is if the end points are included. Use a regular parenthesis ( to not include an endpoint, and use a square bracket [ to include the endpoint.

These examples are of the possibilities of ways to talk about the numbers between two and four:

(2,4) - Does not include 2 or 4
[2,4] - includes both 2 and 4
(2,4] - includes 4, but not 2
[2,4) - includes 4, but not 2

Answer 4

...using parentheses () and blocks[ ] we define an interval from one endpoint to the other ...parentheses (not inclusive) blocks [ include]

neg & positive infinity are always used with parentheses....

examples ( -21 < x < 16 ) ..= (-21,16)
.................( -3<= x < 14) ...= [-3 , 14) 3 included, 14 not