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Stairway to Data, Step 2: Numerics Expand / Collapse
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Posted Thursday, May 12, 2011 9:09 PM


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Comments posted to this topic are about the item Stairway to Data, Step 2: Numerics

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Post #1108175
Posted Wednesday, May 18, 2011 1:07 AM
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The mathematical notation for repeating decimals is to put a bar over the digits in the decimal fraction which form the repeating group. Unlike fractions, there is no way to convert them into floating point or fixed decimal numbers without some loss.

Didn't you mean "like fractions" ?. It seems to me that, mathematically, any number with periodical decimal development can be set as a fraction. For example 1.35... = 1 + 35/99.
Post #1110732
Posted Wednesday, May 18, 2011 4:16 AM
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Nice read, thanks. Be useful for many a kid in maths class too!

Incidentally, did you run a find and replace for many to y, or did I miss something?



Post #1110806
Posted Wednesday, May 18, 2011 9:08 AM
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I've always thought that there was some fallacy when subtracting two irrational numbers to come up with a rational number (9.99... - .99 = 9). I don't have the training to prove or disprove it; it's just a gut feeling.
Post #1111076
Posted Wednesday, May 18, 2011 10:49 AM
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Stephen_W_Dodd (5/18/2011)
I've always thought that there was some fallacy when subtracting two irrational numbers to come up with a rational number (9.99... - .99 = 9). I don't have the training to prove or disprove it; it's just a gut feeling.


They're actually rational - the digits after the decimal have a repeating pattern. But subtracting an irrational number from another irrational number can easily end up as a rational number: if the first irrational number was (1 + v2) and the second was v2, then subtracting the second from the first results in 1. But subtracting two rationals from each other will always result in another rational number, since the set of rationals is closed under addition.

Post #1111191
Posted Wednesday, May 18, 2011 1:54 PM
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What did you mean by "v2, p"? I figured "pi" for "p", but what is "V2"?
Post #1111330
Posted Wednesday, May 18, 2011 1:57 PM
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In relation to "mathematically, any number with periodical decimal development can be set as a fraction." -- I tend to disagree. There are numbers (like sq root of 2 -- and pi) that I seriously doubt can be expressed as a sum of a rational number and a fraction.

Might be interesting to try to prove that but I'm already 68 yrs old and I don't think I have enough time.

Oops! I forgot -- Pi and Sq Root of 2 do not have repeating patterns. So what I said did not apply to the prev statement i quoted.

Pi & Sq root of 2 are true irrational numbers.
Post #1111332
Posted Thursday, May 19, 2011 1:24 AM
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Henry B. Stinson (5/18/2011)
In relation to "mathematically, any number with periodical decimal development can be set as a fraction." -- I tend to disagree. There are numbers (like sq root of 2 -- and pi) that I seriously doubt can be expressed as a sum of a rational number and a fraction.

Might be interesting to try to prove that but I'm already 68 yrs old and I don't think I have enough time.

Oops! I forgot -- Pi and Sq Root of 2 do not have repeating patterns. So what I said did not apply to the prev statement i quoted.

Pi & Sq root of 2 are true irrational numbers.


To prove that (Sq root of 2) can not be set as a rational fraction is very easy :
If it could be set, let a/b be that fraction (a and b being coprimes).
(a/b)2 = 2 by definition.

so a2 = 2 b2, what is impossible, a and b being coprimes.

It is also easy to prove that any number with a periodical decimal development can be set as a fraction :

1/ all cases can be brought back to 0 with the periodical pattern beginnin immediately after the colon.
2/ Let x be the number p the pattern and n the number of its digits.

So x = p/10n + p/102n + ...
This is the sum of a geometrical progression whose first term is p/10n and ratio 1/10n.
That sum is (first term) / (1 - ratio)

So x = p/ (10n - 1).

Qed

Sorry, I'm only 61



Post #1111499
Posted Thursday, May 19, 2011 1:55 PM
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Very Cool!

Next you'll be sending me the solution to Fermat's Last Theorem (without looking it up). :)
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