Interval Notation Formula
The Interval notation formula is introduced in Mathematics. To understand the formula we must first understand what set and real numbers are. Because it will help us to understand the interval notation formula in an easy way, which helps to clearly sort out the problem. Sets are a group of interrelated and well-explained elements. In interval notation formula the first term is known to us, Now come up to real numbers. What real numbers are? If we draw a number line which contains both positive numbers and negative numbers, on the number line we write zero on the centre and when we extend towards the right side of the number line it will be called as a positive side of the number line.
From one to infinity the numbers can be written. And when we extend on number line towards the left side we will write all the negative numbers from one to infinity. So by this, we can say that any number which we can write on a number line are called real numbers. negative numbers, numbers with decimal, square root numbers can also be marked or shown on the number line to check visit. The real numbers can be defined as the rational numbers and irrational numbers shown on the number line. This is the second term we must know for the interval notation formula.
Important terms in Interval Notation Formula.
In interval notation formula the three terms are very important they are as follows
1.inequalities
The interval notation is important to learn about. Inequality means greater than >, smaller than <, greater than or equal to >(diagram 1) < smaller than or equal to. For example (diagram 3) x is greater than or equal to three.
2. Number line
when we draw a number line with positive side and negative side, when we want to mark our end value we will mark it on a number line with pack circle. And when we do not want to mark our end value we will mark it with unpack or open circle. (diagram 5)
3.Interval notation marks
Interval notation is written with square brackets [ ] and round brackets ( ).
and the Initial or beginning value and end or last value are considered.
For example 6, 14 here 6 is our initial value and 14 is our end value. we do not write the beginning value six, we will write only 14.
When we use square brackets and round brackets.
- when we involve end values we use [ ] square brackets.
- when we do not involve end values we use ( ) round brackets.
(diagram 4.1) when the value six is marked with unpack circle on the number line.
(diagram 4.2) when the value six is marked with pack circle on the number line.
(diagram 4.3) when the value 14 is marked with unpack circle on the number line.
(diagram 4.4) when the value 14 is marked with pack circle on the number line.
one point is also taken into consideration is that the greater than values and smaller than values all are written in round brackets with unpack marked circle. and all the greater than or equal to and smaller than or equal to numbers are written in square brackets with pack marked circle. Hope you have understood the basics of Interval Notation Formula, taught in a basic manner.
Interval notation types:
1. Closed Interval
When we take two real numbers like c and d, d is greater than c. c
2. Open Interval
Here in Open interval also when we take two real numbers like c and d then here we say d is greater than c. c<d, Then the c<x
Various applications are also developed to use and take out the result, these are like you have to enter the interval only and it will give you the results of it. The result is always given in such format as it shows you the result on a number line, every step is clearly shown to you, and the result also gives in graphical representation. Sometimes it proves to be a time-saving process and results are always found to be accurate and correct.