# What are 'intervals'? Explain with examples (i.e sets).

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### 1 Answer

The intervals are sets of numbers. All the numbers that have the property to be located between the endpoints of the interval are elements of the set.

Examples:

The open interval (-1;5) is the set of real numbers x that have the property:

-1 < x < 5

All the real numbers located between -1 and 5, excluding -1 and 5, are the elements of the interval (-1,5).

(-1,5) = {x belongs to R / -1 < x < 5 }

The closed interval [-5,10] is the set of real numbers x that have the property:

-5 =< x =< 10

[-5,10] = {x belongs to R / -5 =< x =< 10}

All the real numbers located between -5 and 10, including -5 and 10, are the elements of the interval [-5,10].

There are included also the intervals that have an open endpoint and a closed endpoint:

(a,b] or [a,b)

That means the following:

(a,b] = {x belongs to R / a< x =< b}

[a,b) = {x belongs to R / a =< x < b}

There is the possibility for one of the endpoints to be infinite. This means that the set has no limit to the left or to the right, depending what endpoint is infinite.