- #1

icystrike

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Irrational Numbers are contained by infinite numerical values?

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- Thread starter icystrike
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In summary, irrational numbers are numbers that cannot be written as fractions and have an infinite number of digits after the decimal point. However, even some rational numbers can have an infinite number of digits after the decimal point, such as 1/7 or 1/3. This depends on the base of the number system used. And while every irrational number has an infinite non-repeating decimal expansion, rational numbers can have either a finite or infinite repeating decimal expansion. The representation of numbers as decimals is based on conventions and does not necessarily reflect the true nature of the numbers themselves.

- #1

icystrike

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Irrational Numbers are contained by infinite numerical values?

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- #2

Ya$amin

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huh?!i didn't get what u mean:D

- #3

icystrike

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meaning if we would to write a irrational number out , we need a infinite number of digits?

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g_edgar

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icystrike said:meaning if we would to write a irrational number out , we need a infinite number of digits?

Do you care? If we write out 1/7 we would require an infinite number of digits.

- #5

Borek

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Depends on the base of the number system used. 1/7 is 0.1_{7}, 1/3 is 0.1_{3}, both require infinite number of digits if they are to be written base 10.

*Edit: do you hate it when you make an idiot out of yourself just because you think in your first language when you should in English? I do. Irrational as it sounds, I was all the time thinking about rational numbers.*

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- #6

zgozvrm

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On the other hand, just because there are an infinite number of digits following the decimal point, doesn't mean that the the value is irrational. (0.111111111... can be written as 1/9, so it is rational, whereas [tex]\pi, \: e, \: and \: \sqrt{2}[/tex] are all examples of irrational numbers).

- #7

Mark44

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1/7 can also be written as 0.06666666...Borek said:Depends on the base of the number system used. 1/7 is 0.1_{7}, 1/3 is 0.1_{3}, both require infinite number of digits if they are to be written base 10.

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Landau

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Hurkyl

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I can write [itex]\sqrt{2}[/itex] with two symbols:icystrike said:meaning if we would to write a irrational number out , we need a infinite number of digits?

The

- #10

gmax137

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Hurkyl said:don't forget about the infinitely many zeros!

That's what I was thinking. We can write "2" without all the zeroes (2.000000...) because

- #11

qntty

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maybe you'd be interested in http://www.dpmms.cam.ac.uk/~wtg10/decimals.html" article on the topic of thinking about numbers as infinite decimals

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- #12

icystrike

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hey qntty ! thanks for your help. its greatly appreciated!

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HallsofIvy

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Then I realized that he had been taught "a rational number can be written as a terminating or repeating decimal" as the

Irrational numbers are numbers that cannot be expressed as a simple fraction or ratio of two integers. They are infinite decimal values that do not repeat or terminate.

Rational numbers can be expressed as a simple fraction or ratio, while irrational numbers cannot. Rational numbers also have a finite number of decimal places, while irrational numbers have an infinite number of decimal places.

One of the most famous examples of an irrational number is π (pi). Other examples include √2 (the square root of 2), √3 (the square root of 3), and e (Euler's number).

Irrational numbers are used in many real-life applications, such as in geometry, physics, and engineering. For example, the value of π is used in calculating the circumference and area of a circle.

Yes, irrational numbers can be approximated by rounding off the decimal values. However, this will result in a less precise value, as the decimal places of irrational numbers are infinite.

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