Can anyone explain the interval, roster, and the set builder notation to me please?

Question

dinamix · Answer

interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. For example, the set of all numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0 and 1, as well as all numbers between them @PinkSapphire

pinksapphire · Answer

Okay, so is there an infinite amount of numbers in that set?

dinamix · Answer

i want ask u how many numbers we have $$x \in[0; 1]$$

dinamix · Answer

@PinkSapphire

pinksapphire · Answer

Any number between 0 and 1 including 0 and 1?

dinamix · Answer

yup this is it

pinksapphire · Answer

Okay, thanks :)

pinksapphire · Answer

Do you know how to do the other ones?

zzr0ck3r · Answer

Yes there are an infinite amount of numbers in that interval. In fact any interval that has more than one number has the same amount of numbers as there are number!!! WTH??>

pinksapphire · Answer

:)

zzr0ck3r · Answer

Let us look at examples of all three notations.

We will consider all of the numbers between 1 and 2, and we will NOT include 1 and 2.

Set builder notation:

$$\{x\in \mathbb{R} \mid 1<x<2\}$$

This says all real numbers x such that 1< x< 2

Interval notation:

(1,2)


Roster notation:

We cant use that here!!!! there is no way to list all of the numbers between 1 and 2

So we use another example for Roster notation. Consider the integers between -3 and 4 and include -3 and 4.

$\{-3, -2, -1, 0, 1, 2, 3, 4\}$

pinksapphire · Answer

Okay, that makes sense.