Question

Please Explain the irrational numbers and rational numbers and differences between them and also
explain irrational functions.

Answer 1

A number is rational if it can be written as the quotient of two integers.

Answer 2

This is why the set of rational numbers is denoted \(\mathbb Q\) for quotient.

Answer 3

Please explain @nbouscal .

Answer 4

other than the number itself over 1

Answer 5

example...2 is rational because i can express it as 4/2

Answer 6

For any rational number there is a \(p\) and \(q\) with \(p,q\in\mathbb Z\) such that the rational number can be written as \(\dfrac p q \)

Answer 7

Please mention differences between rational and irrational numbers also.

Answer 8

Irrational numbers are simply numbers that are not rational.

Answer 9

pi cannot be expressed as a quotient even though 22/7 is near therefore it is irrational

Answer 10

Some more examples ....@lgbasallote

Answer 11

The simplest proof of an irrational number is the one for \(\sqrt2\). http://www.homeschoolmath.net/teaching/proof_square_root_2_irrational.php shows the standard proof, due to the Greeks.

Answer 12

ALL integers are rational numbers

Answer 13

the integers are -1, -2, -3, 0, 1, 2, 3, etc

Answer 14

Decimal numbers that terminate are rational, because they can be written as a fraction. For example, 2.231 can just be written as 2231/1000. This is the case for any decimal that terminates.

Answer 15

What about 1/3...................?@nbouscal @lgbasallote @ParthKohli

Answer 16

some decimals that dont terminate can also be expressed as fractions...for example 0.333333 can be expressed as 1/3

Answer 17

1/3 is a quotient of two integers, so it is a rational number.

Answer 18

that is rational because 1 amd 3 are integers

Answer 19

do you get it now?

Answer 20

If you want to get even more fun you can look at the transcendental numbers, they are even more crazy than the irrational numbers. Irrational numbers that are not transcendental are called algebraic, they can be found as the roots of polynomials. There are all sorts of fun proofs to be read in this area of mathematics.

Answer 21

lol why make it confusing :p

Answer 22

Of coarse @lgbasallote is right.

Answer 23

the kid doesnt understand rational and irrational and you're suggesting "fun" :p

Answer 24

Also worth noting is that the union of the rational and irrational numbers forms the real numbers, \(\mathbb R\), which is the set that you usually work in. You can also go further to \(\mathbb C\), the complex numbers. And then even further than that :)

Answer 25

I'm giving him an idea of the cool stuff ahead, it doesn't just stop at rational and irrational :P

Answer 26

sometimes it's nicer to live in fantasies for some time

Answer 27

1/3 has recurring digits but is still expressed as a quotient of two integers, so it is rational.

Answer 28

i'd rather take the blue pill than the red