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Stairway to Data, Step 2: Numerics
Stairway to Data, Step 2: Numerics
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CELKO
CELKO
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
Books in Celko Series for Morgan-Kaufmann Publishing
Analytics and OLAP in SQL
Data and Databases: Concepts in Practice
Data, Measurements and Standards in SQL
SQL for Smarties
SQL Programming Style
SQL Puzzles and Answers
Thinking in Sets
Trees and Hierarchies in SQL
Post #1108175
Roland C
Roland C
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
RichB
RichB
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
Stephen_W_Dodd
Stephen_W_Dodd
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
Aleph_0
Aleph_0
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
Henry B. Stinson
Henry B. Stinson
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
Henry B. Stinson
Henry B. Stinson
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
Roland C
Roland C
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 a
2
= 2 b
2
, 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/10
n
+ p/10
2n
+ ...
This is the sum of a geometrical progression whose first term is p/10
n
and ratio 1/10
n
.
That sum is (first term) / (1 - ratio)
So x = p/ (10
n
- 1).
Qed
Sorry, I'm
only
61
Post #1111499
Henry B. Stinson
Henry B. Stinson
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). :)
Post #1112000
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