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shahzadjalbani
 2 years ago
Please Explain the irrational numbers and rational numbers and differences between them and also
explain irrational functions.
shahzadjalbani
 2 years ago
Please Explain the irrational numbers and rational numbers and differences between them and also explain irrational functions.

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nbouscal
 2 years ago
Best ResponseYou've already chosen the best response.1A number is rational if it can be written as the quotient of two integers.

nbouscal
 2 years ago
Best ResponseYou've already chosen the best response.1This is why the set of rational numbers is denoted \(\mathbb Q\) for quotient.

shahzadjalbani
 2 years ago
Best ResponseYou've already chosen the best response.0Please explain @nbouscal .

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0other than the number itself over 1

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0example...2 is rational because i can express it as 4/2

nbouscal
 2 years ago
Best ResponseYou've already chosen the best response.1For any rational number there is a \(p\) and \(q\) with \(p,q\in\mathbb Z\) such that the rational number can be written as \(\dfrac p q \)

shahzadjalbani
 2 years ago
Best ResponseYou've already chosen the best response.0Please mention differences between rational and irrational numbers also.

nbouscal
 2 years ago
Best ResponseYou've already chosen the best response.1Irrational numbers are simply numbers that are not rational.

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0pi cannot be expressed as a quotient even though 22/7 is near therefore it is irrational

shahzadjalbani
 2 years ago
Best ResponseYou've already chosen the best response.0Some more examples ....@lgbasallote

nbouscal
 2 years ago
Best ResponseYou've already chosen the best response.1The 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.

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0ALL integers are rational numbers

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0the integers are 1, 2, 3, 0, 1, 2, 3, etc

nbouscal
 2 years ago
Best ResponseYou've already chosen the best response.1Decimal 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.

shahzadjalbani
 2 years ago
Best ResponseYou've already chosen the best response.0What about 1/3...................?@nbouscal @lgbasallote @ParthKohli

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0some decimals that dont terminate can also be expressed as fractions...for example 0.333333 can be expressed as 1/3

nbouscal
 2 years ago
Best ResponseYou've already chosen the best response.11/3 is a quotient of two integers, so it is a rational number.

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0that is rational because 1 amd 3 are integers

nbouscal
 2 years ago
Best ResponseYou've already chosen the best response.1If 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.

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0lol why make it confusing :p

shahzadjalbani
 2 years ago
Best ResponseYou've already chosen the best response.0Of coarse @lgbasallote is right.

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0the kid doesnt understand rational and irrational and you're suggesting "fun" :p

nbouscal
 2 years ago
Best ResponseYou've already chosen the best response.1Also 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 :)

nbouscal
 2 years ago
Best ResponseYou've already chosen the best response.1I'm giving him an idea of the cool stuff ahead, it doesn't just stop at rational and irrational :P

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0sometimes it's nicer to live in fantasies for some time

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.01/3 has recurring digits but is still expressed as a quotient of two integers, so it is rational.

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0i'd rather take the blue pill than the red
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