SQLServerCentral / Article Discussions / Article Discussions by Author / Discuss content posted by Joe Celko / Stairway to Data, Step 2: Numerics / Latest PostsInstantForum.NET v2.9.0SQLServerCentralhttp://www.sqlservercentral.com/Forums/notifications@sqlservercentral.comThu, 17 Apr 2014 08:57:04 GMT20RE: Stairway to Data, Step 2: Numericshttp://www.sqlservercentral.com/Forums/Topic1108175-1604-1.aspxVery Cool! Next you'll be sending me the solution to Fermat's Last Theorem (without looking it up). :)Thu, 19 May 2011 13:55:32 GMTHenry B. StinsonRE: Stairway to Data, Step 2: Numericshttp://www.sqlservercentral.com/Forums/Topic1108175-1604-1.aspx[quote][b]Henry B. Stinson (5/18/2011)[/b][hr]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.[/quote]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)[sup]2[/sup] = 2 by definition.so a[sup]2[/sup] = 2 b[sup]2[/sup], 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[sup]n[/sup] + p/10[sup]2n[/sup] + ...This is the sum of a geometrical progression whose first term is p/10[sup]n[/sup] and ratio 1/10[sup]n[/sup].That sum is (first term) / (1 - ratio)So x = p/ (10[sup]n[/sup] - 1).QedSorry, I'm [i]only[/i] 61 ;-)Thu, 19 May 2011 01:24:09 GMTRoland CRE: Stairway to Data, Step 2: Numericshttp://www.sqlservercentral.com/Forums/Topic1108175-1604-1.aspxIn 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.Wed, 18 May 2011 13:57:36 GMTHenry B. StinsonRE: Stairway to Data, Step 2: Numericshttp://www.sqlservercentral.com/Forums/Topic1108175-1604-1.aspxWhat did you mean by "v2, p"? I figured "pi" for "p", but what is "V2"?Wed, 18 May 2011 13:54:38 GMTHenry B. StinsonRE: Stairway to Data, Step 2: Numericshttp://www.sqlservercentral.com/Forums/Topic1108175-1604-1.aspx[quote][b]Stephen_W_Dodd (5/18/2011)[/b][hr]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.[/quote]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.Wed, 18 May 2011 10:49:34 GMTAleph_0RE: Stairway to Data, Step 2: Numericshttp://www.sqlservercentral.com/Forums/Topic1108175-1604-1.aspxI'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.Wed, 18 May 2011 09:08:51 GMTStephen_W_DoddRE: Stairway to Data, Step 2: Numericshttp://www.sqlservercentral.com/Forums/Topic1108175-1604-1.aspxNice 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?Wed, 18 May 2011 04:16:24 GMTRichBRE: Stairway to Data, Step 2: Numericshttp://www.sqlservercentral.com/Forums/Topic1108175-1604-1.aspx[quote]The mathematical notation for repeating decimals is to put a bar over the digits in the decimal fraction which form the repeating group.[i] Unlike fractions,[/i] there is no way to convert them into floating point or fixed decimal numbers without some loss.[/quote] Didn't you mean "[b]like [/b]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.Wed, 18 May 2011 01:07:19 GMTRoland CStairway to Data, Step 2: Numericshttp://www.sqlservercentral.com/Forums/Topic1108175-1604-1.aspxComments posted to this topic are about the item [B]<A HREF="/articles/Stairway+Series/Numerics+and+SQL/72659/">Stairway to Data, Step 2: Numerics</A>[/B]Thu, 12 May 2011 21:09:01 GMTCELKO