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 Posted Thursday, May 12, 2011 9:09 PM
 SSCommitted Group: General Forum Members Last Login: Yesterday @ 4:57 PM Points: 1,945, Visits: 3,498
 Comments posted to this topic are about the item Stairway to Data, Step 2: Numerics Books in Celko Series for Morgan-Kaufmann PublishingAnalytics and OLAP in SQL Data and Databases: Concepts in Practice Data, Measurements and Standards in SQLSQL for SmartiesSQL Programming Style SQL Puzzles and Answers Thinking in SetsTrees and Hierarchies in SQL
Post #1108175
 Posted Wednesday, May 18, 2011 1:07 AM
 SSCrazy Group: General Forum Members Last Login: Yesterday @ 11:54 PM Points: 2,557, Visits: 605
 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
 Ten Centuries Group: General Forum Members Last Login: Thursday, April 2, 2015 10:13 AM Points: 1,072, Visits: 934
 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
 SSC Eights! Group: General Forum Members Last Login: Monday, February 2, 2015 9:35 AM Points: 952, Visits: 553
 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
 SSC Rookie Group: General Forum Members Last Login: Wednesday, October 1, 2014 10:49 AM Points: 30, Visits: 124
 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
 Valued Member Group: General Forum Members Last Login: Monday, April 20, 2015 10:42 AM Points: 71, Visits: 52
 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
 Valued Member Group: General Forum Members Last Login: Monday, April 20, 2015 10:42 AM Points: 71, Visits: 52
 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
 SSCrazy Group: General Forum Members Last Login: Yesterday @ 11:54 PM Points: 2,557, Visits: 605
 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).QedSorry, I'm only 61
Post #1111499
 Posted Thursday, May 19, 2011 1:55 PM
 Valued Member Group: General Forum Members Last Login: Monday, April 20, 2015 10:42 AM Points: 71, Visits: 52
 Very Cool! Next you'll be sending me the solution to Fermat's Last Theorem (without looking it up). :)
Post #1112000
 Posted Tuesday, September 30, 2014 9:30 PM
 Forum Newbie Group: General Forum Members Last Login: Tuesday, September 30, 2014 9:27 PM Points: 1, Visits: 0
 V2 is the point on the tarmac where rotation occurs Sorry, I am not a mathematician, just a bad joker...
Post #1621422

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