LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

SETS - INTERVAL

**Intervals
–**

**Many infinite
sets, such as the real numbers, cannot be represented in roster form. There are
other methods of representing these sets. For example, the number line
represents the set of all real numbers.**

**The set of
real numbers between 4 & 7, which is also an infinite set, can be
represented on a number line or by an
inequality.**

**An interval is
the set of all numbers between two end points, such as 4 & 7.**

**In Interval
notation the symbols [and] are used to include an end point from an interval,
and the symbols (and) are used to exclude an endpoint from an interval, e.g,**

**(4, 7) the
set of real numbers between 4 and 7 but not including 4 & 7**

**The notation
[ ] indicates closed interval as it includes the end points also while the
notation ( ) is called an open interval as it does not include the endpoints of
the interval**

**A finite
interval is said to be closed if it contains both of its endpoints,
half-open if it contains one endpoint but not the other, and open if
it contains neither endpoint. The endpoints are also called boundary points when they make up the interval’s boundary. The remaining point of the
interval are interior points and together comprise the interval’s interior.
Infinite intervals are closed if they contains a finite end point, and open
otherwise. The entire real line R is an infinite interval that is both open and
closed.**

**An interval
that extends forever in the positive direction goes to infinity (∞), and an
interval that extends forever in the negative direction goes to negative
infinity (- ∞).**

**There are
some example are given blow for your better understanding –**

**1) Let, B = {3, 4, 5, 6, 7, 8}. Insert the appropriate symbol ∈ or ∉ in the blank spaces.**

**(i) 6…………B **

**Ans.) 6
∈ B (because 6 belongs to set B)**

**(ii) 2…………….B**

**Ans.) 2 ∉ B (because 2 is not belongs to set B)**

**(iii) 4……………B**

**Ans.) 4 ∈
B (because 4 belongs
to set B)**

**(iv) 10…………..B**

**Ans.) 10 ∉
B (because 10 is not
belongs to set B)**

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