Question

Set of all the real number greater than 8 but less than 65?

Answer 1

Answer:

What is the set notation of the set of all real numbers greater than 8, but less than 65?

There are various conventions around set notation which mean that there is no "the" set notation, but I would write:

{x∈R:8<x<65}

If the context of a set of Real numbers is clear, this interval can also be written simply as (8,65) .

In both cases the boundary numbers are excluded: I have interpreted greater than as strictly greater than and less than as strictly less than. One notation for including one or both boundaries is:

[a,b]={x∈R:a≤x≤b}

(a,b]={x∈R:a<x≤b}

[a,b)={x∈R:a≤x<b}

Let the no be, x

A/Q,

x>8——(1)

x<65——(2)

From equation (1) & (2) we get,

8<x<65

When it is written on set notation

A={x: 8<x<65,x€R}

Where R is set of Real no.

Another method is using interval

In interval method we can observed that,

The no x is the no between 8 and 65 but the boundary no(8 & 65) are not included.

So its an open interval

A=(8,65)

It is the easiest way to write real no set notation in case of interval

Let the number be x.

x is greater than 8. So,

x>8 or 8<x⋯(1)

x is less than 65. So,

x<65⋯(2)

The number x belongs to the set of real numbers. Therefore,

x∈R⋯(3)

where ∈ symbol represents 'belongs to'.

Combining conditions (1) and (2) gives:

8<x<65

Now, we shall write the set builder form. Have a name for the set, say A. We combine conditions (1) and (2) (interval) and embed the condition (3) in it (restriction/domain).

A={x:8<x<65,x∈R}

where, the symbol : denotes 'such that'. The above notation is read as:

“ Set of all x such that x is between 8 and 65 and x belongs to the set of real numbers.”