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

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

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

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

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

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

nbouscal Group TitleBest ResponseYou've already chosen the best response.1
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 \(\dfrac p q \)
 2 years ago

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

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

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

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

nbouscal Group TitleBest ResponseYou've already chosen the best response.1
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.
 2 years ago

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

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

nbouscal Group TitleBest ResponseYou've already chosen the best response.1
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.
 2 years ago

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

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

nbouscal Group TitleBest ResponseYou've already chosen the best response.1
1/3 is a quotient of two integers, so it is a rational number.
 2 years ago

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

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
do you get it now?
 2 years ago

nbouscal Group TitleBest ResponseYou've already chosen the best response.1
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.
 2 years ago

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

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

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

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

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

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

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
1/3 has recurring digits but is still expressed as a quotient of two integers, so it is rational.
 2 years ago

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