In the previous post we have discussed about Is 0 a Natural Number and In today's session we are going to discuss about Irrational Number, We have various types of numbers on our number line in mathematics, like, real numbers, whole numbers, rational, irrational number, complex, natural, integers, etc. But now, our most priority is irrational number which is nothing but a number which cannot be written in the form of a/b or fraction or a quotient, where a and b are integers and b is not equal to zero.
The decimal expansion of an irrational number neither ends or terminates itself nor it repeats some same sequence of digits over and again.
Since irrational number cannot be represented in the form of a simple fraction, so we can say that it is not a rational number, which is just the opposite of rational number as it can be expressed in the form of a quotient or a fraction like a/b.
Irrational numbers consists of numbers like e (Euler’s number), π (pi), √2 (square root of 2), φ (golden ratio), etc.
Whereas irrational numbers cannot be represented like 5/2, 2.14, 1/10, which rational numbers can.
According to the Cantor’s proof: as we that our number line on the coordinate plane is full of real numbers, which means they are uncountable and since we can count rational numbers, so we can finally conclude that almost all the real numbers are irrational in nature and not rational. But on the other side we have to say that rational numbers are dense in nature, which means that between any two integers there are many rational numbers but still they can be counted.
There are many facts which irrational numbers give, like when we calculate the ratio of lengths of two line segments and if it comes out to be an irrational number, then those line segments are known as incommensurable, which means that they have no common measures to share.
In order to get help in the topics: irrational number, what is the pythagorean theorem you can prefer cbse books for class 9 availble online for free.
The decimal expansion of an irrational number neither ends or terminates itself nor it repeats some same sequence of digits over and again.
Since irrational number cannot be represented in the form of a simple fraction, so we can say that it is not a rational number, which is just the opposite of rational number as it can be expressed in the form of a quotient or a fraction like a/b.
Irrational numbers consists of numbers like e (Euler’s number), π (pi), √2 (square root of 2), φ (golden ratio), etc.
Whereas irrational numbers cannot be represented like 5/2, 2.14, 1/10, which rational numbers can.
According to the Cantor’s proof: as we that our number line on the coordinate plane is full of real numbers, which means they are uncountable and since we can count rational numbers, so we can finally conclude that almost all the real numbers are irrational in nature and not rational. But on the other side we have to say that rational numbers are dense in nature, which means that between any two integers there are many rational numbers but still they can be counted.
There are many facts which irrational numbers give, like when we calculate the ratio of lengths of two line segments and if it comes out to be an irrational number, then those line segments are known as incommensurable, which means that they have no common measures to share.
In order to get help in the topics: irrational number, what is the pythagorean theorem you can prefer cbse books for class 9 availble online for free.
No comments:
Post a Comment