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Originally Posted by Racoon Can anyone help explain Irrational Numbers? |
Several members have done a pretty good job already:
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Originally Posted by ronthepon …Numbers which are infinite decimals which do not repeat. |
and
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Originally Posted by Qfwfq Rational numbers are a ratio, which means a ratio of two of the previously defined integer numbers.
2/3, 7/5, 6/35 |
Since any terminating decimal number can be written as a ratio (eg: 1.234 = 1234/1000), and, slightly less obviously, so can any infinitely repeating decimal number (eg: 0.333… = 1/3), these are in effect the same, correct definition of an irrational number.
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Originally Posted by Racoon Pi = irrational |
Correct
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Golden Ratio = irrational? --> Craig had stated (5^.5 + 1) / 2
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Yes –

is irrational, so the golden ratio is too
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Fibionachi Sequence = irrational?
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No, at least not usually. The ratio of terms of the 2 (or any) Fibonachi sequence is rational, because the terms of any ”standard” Fibonachi sequence (eg: 1,1,2,3,5,8,…) are integers.
You
could create a weird Fibonachi sequence where the ration of terms is irrational so that this isn’t true, such as: 1,

,

,

,

,…
To head off any potential confusion, let me expand a bit on something in Ron’s post:
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Originally Posted by ronthepon You can never use these [irrational] numbers in linear equations properly without using approximation methods. |
While it’s true that an irrational number can only be approximated by a rational number, irrational numbers can be used freely in equations without resorting to approximation. An expression involving Irrational numbers may even have a rational value, eg:
It’s important, I think, to note that there’s nothing necessarily unknown or inexact about most irrational numbers, just that they can’t be written as fractions of integers. They’re less
convient, but this is due to coincidental qualities - such as most electronic calculators and computers storing numbers in some way using integers, and that it’s not as easy in most text editing/displaying software to displaying

as it is 1.25 – not an inate quality of irrational numbers themselves.
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