Wikipedia:Reference desk/Archives/Mathematics/2007 September 9

= September 9 =

Maths is about numbers
Is it true that Maths is about numbers just like Agatha Christie murder mysteries is about the English alphabets? I heard someone use that phrase but I thought that they were just jesting. Is there any truth to that phrase? 211.28.131.182 09:07, 9 September 2007 (UTC)
 * I wouldn't say this phrase is very accurate, but it has a point and I do not believe it was said in jest. The point is that math is about much more than just numbers. Granted, numbers of all sorts are very important in almost any aspect of mathematics, but not everything revolves around them. -- Meni Rosenfeld (talk) 11:03, 9 September 2007 (UTC)
 * To be absolutely clear, Agatha Christie's murder mysteries are not about the English alphabet, even though that alphabet does play a major role in how they are written and read. See also our Mathematics article, which tries to get across what maths is about. --Lambiam 12:14, 9 September 2007 (UTC)
 * The A.B.C. Murders? —Blotwell 14:52, 10 September 2007 (UTC)
 * I suspect that if the OP's doubts had been about the second part, he would have asked the question at Reference desk/Humanities. -- Meni Rosenfeld (talk) 12:26, 9 September 2007 (UTC)
 * But perhaps (what do I know?) the questioner assumes that the truth of the second part is raised above all doubt, and wonders if the first part is, likewise, true. --Lambiam 14:07, 9 September 2007 (UTC)
 * I would say that it is certainly true that modern mathematics is not just about numbers, and that numbers play a very small role in much of modern math. The quote perhaps exagerates the case, but I think the sentiment behind it is valid. Saying what mathematics actually is about is rather hard, but I would suggest that words like "abstraction", and "structure", and "structural relationships" are far loser than "number". See, for instance, category theory where the fundamental things under consideration are the (directed) relationships between objects, and the structures that result, and then note that category theory provides a language and perspective that is applicable to almost all of modern mathematics. Numbers don't need to enter into it. -- Leland McInnes 15:28, 9 September 2007 (UTC)

Number bases
How do you solve this equation? xyyz(base 5) + xyyz (base 7)=xyyz (base 8) —Preceding unsigned comment added by 124.82.104.162 (talk) 15:42, 9 September 2007 (UTC)


 * I take it that each of those numbers is a digit? Well... a number in base n is represented by the digit times a power of n, so the first number would be z * 5^0 + y * 5^1 + y*5^2 + x*5^3 in base 10... does that help? Gscshoyru 15:52, 9 September 2007 (UTC)

Sounds like constrain logic programming.

x*5^3 + y*5^2 + y*5^1 + z + x*7^3 + y*7^2 + y*7^1 + z = x*8^3 + y*8^2 + y*8^1 + z


 * x in {0,1,2,3,4}
 * y in {0,1,2,3,4}
 * z in {0,1,2,3,4}

Concentrate on z where z + z = a * 8 + z where a in {0,1}

We have z in {0} so z must be zero.

alternatively you can use the brute force method which is not that hard as there is only 125 different combinations. 202.168.50.40 00:48, 10 September 2007 (UTC)


 * "z + z = a * 8 + z" is wrong. PrimeHunter 03:28, 10 September 2007 (UTC)


 * Simplfying the above we get
 * 14y + z = 44x
 * Clearly z must be even; and so must be 0, 2, or 4. Also, increasing (or decreasing) x and y by 7 and 22, respectively (since gcd(14,44) = 2), or any multiple thereof will not change the truth of the equation.


 * If z = 0, then x = y = 0 is a solution (but we don't want x to be 0). The next higher solution is (7, 22, 0) which is outside our bounds.
 * If z = 2, then 44x - 14y = 2. By the extended Euclidean algorithm we get x = 1, y = 3. (1, 3, 2) is a solution. Increasing or decreasing x by 7 will put us outside our bounds.
 * If z = 4, then 44x - 14y = 4. Doubling the above, we see that x = 2, y = 6 works. But y = 6 is outside the bounds. And increasing or decreasing x by 7 will also go outside the bounds. So this doesn't work.
 * So we conclude the only solution is x = 1, y = 3, z = 2. --152.75.18.108 22:38, 10 September 2007 (UTC)

Chess books
For a number of years I have been playing chess casually and have taken a liking to the game, and I wish to take my game to the next level. However, I have no theoretical background. I was hoping that you guys could recommend some good chess books to improve all aspects of the game (opening repertoire especially). Thanks a lot! —Preceding unsigned comment added by 70.52.45.191 (talk) 19:25, 9 September 2007 (UTC)


 * You could try the references at chess openings (disclaimer: I know nothing of chess) Algebraist 13:30, 10 September 2007 (UTC)


 * Re openings, generalising, there are three types of books about chess openings. There are the encyclopedic (of which Batsford's Modern Chess Openings is probably the best, I think it's now in its 14th edition), those that deal with a "family" of openings and those that pick over the bones of a single line. I'd recommend you start with Batsford, but try and find a 2nd hand copy in good condition - theory of the main lines doesn't move on so fast that an out of date edition makes a huge difference. Use Batsford to develop at least a basic understanding of the most common openings - then use your new knowledge to find the right specialist books to take you on. See also Category:Chess books and Chess endgame literature --Dweller 13:55, 10 September 2007 (UTC)

TI-84+ equation solver
When I'm using the TI-84 Equation Solver (Math>Solver) after I enter in an equation and enter a guess then hit Alpha+Solve, it gives me an answer but one line down, it says "left-rt=0". What does "left-rt=0" mean? Thanks. Acceptable 23:03, 9 September 2007 (UTC)
 * er? Lefthand side minus righthand size equals zero? 202.168.50.40 00:42, 10 September 2007 (UTC)

Lol, thanks, all those words on the screen confused me. Acceptable 00:59, 10 September 2007 (UTC)