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The integers (from the Latin integer, literally "untouched", hence "whole": the word entire comes from the same origin, but via French) are natural numbers including 0 (0, 1, 2, 3, ...) and their negatives (0, −1, −2, −3, ...). They are numbers that can be written without a fractional or decimal component, and fall within the set {... −2, −1, 0, 1, 2, ...}. For example, 65, 7, and −756 are integers; 1.6 and 1½ are not integers. In other terms, integers are the numbers one can count with items such as apples or fingers, and their negatives, as well as 0. More formally, the integers are the only integral domain whose positive elements are well-ordered, and in which order is preserved by addition. Like the natural numbers, the integers form a countably infinite set. The set of all integers is often denoted by a boldface Z (or blackboard bold , Unicode U+2124 ℤ), which stands for Zahlen (German for numbers, pronounced [ˈtsaːlən]). Integers can be thought of as points on an infinitely long number line.In algebraic number theory, these commonly understood integers, embedded in the field of rational numbers, are referred to as rational integers to distinguish them from the more broadly defined algebraic integers. From Wikipedia under the
GNU Free Documentation License  atm.org.uk 194px x 125px | 6.20kB [source page] God Created the Integers The Mathematical Breakthroughs That Changed History This is a daunting book to pick up it spans almost 1200 pages but then it is also trying to span the complete history of mathematics From Euclid to Turing passing Archimedes  angelo.edu 813px x 508px | 62.50kB [source page] Teacher Talk Details More Details Previous Next Back to Bulletin Board Topics From Yahoo Image Search: "Integers"  scipub.org unknown Mon, 24 Aug 2009 14:37:26 GM Accelerated Search for Gaussian Generator Based on Triple Prime . Integers. . 1Boris S. Verkhovsky and 2Md Shiblee Sadik. 1Department of Computer Science, New Jersey Institute of Technology, USA. 2 Department of Computer Science, ...  java-forums.org dj kourampies Wed, 19 Aug 2009 18:36:30 GM I want to write . integers. (pe a telephone number or ID) into a file. But the method write() of FileWriter seems to support only char, not int. What am.  wiki.bssd.org Dgharst ue, 11 Aug 2009 21:39:42 GM New page: ==Level 7-9 Mental Math Examples== New page. ==Level 7-9 Mental Math Examples== From Google Blog Search: "Integers"  news.google.com Slashdot (DD/MM/YY). For chronologically sorting dates represented as integers I guess YYYMMDD would be handy. by topnob (1195249) news.google.com Printer Ink Cartridges News & Blog This is not like mathematics, where multiplying two negative integers make a positive integer (although mathematics plays a major role in managing your ... news.google.com AZ Central.com They review math concepts such as integers and, in language arts, the basic structure of a story. They also have daily team activities to build friendships. ... and more » From Google News Search: "Integers" How to find the sum of all positive consecutive integers, say from 1 to 48? Q. If A is the set of consecutive positive integers from 1 to 48, B is the sum of even consecutive integers in A and C is the sum of odd consecutive integers in A. Then, B is greater or C+35 is greater? So, is there any short cut method method or formula to find the sum of consecutive integers/consecutive even integers/consecutive odd integers/ consecutive prime numbers, say all within the number 100? Or is there any easy method to find whether sum of even or the sum of odd consecutive numbers is greatest. Thanks Asked by madhu - Mon Sep 17 11:27:02 2007 - - 3 Answers - 0 Comments A. These are triangular numbers: There is a wealth of information in this Wikipedia article. Sufficed to say that the formula is: n(n+1)/2 If n is even, you can pair off each one: 1 + n 2 + (n-1) 3 + (n-2) etc Into n/2 pairs that sum to (n+1). Total: (n/2)(n + 1) = n(n+1)/2 If it's odd, you do the same: 1 + n 2 + n-1 ... Except you can't pair off the middle one. You have (n-1)/2 pairs that sum to (n+1) and a left-over (n+1)/2 that you couldn't pair off. Total: (n-1)(n+1)/2 + (n+1)/2 =(n-1+1)(n+1)/2 = n(n+1)/2 They're called triangular, by the way, because if you're making a triangle (say with pennies) every row you add you have to add on one more than the bottom row you have now. EG: 1+2+3+4 Next row would add 5. Now then, to… [cont.] Answered by cheeser1 - Mon Sep 17 11:34:08 2007 what is the absolute FASTEST way to sort a bunch of integers? Q. I need to be able to sort 1 million integers faster then quicksort. The fastest. I get extra points if it only takes "a[range]" executions. Asked by Antony D - Wed Dec 3 13:35:43 2008 - - 2 Answers - 0 Comments A. There is a faster algorithm than O(n log n) time. The downside is that it requires memory that scales with the range of the integers. The algorithm is called "bucket sort" on wikipedia, and it actually only takes O(n) executions if you use buckets of size 1. The downside, as I said, is that you would need to have one bucket for every integer in the range you're looking at: if your range is from 1 to 1 million, you need an array 1 million long, which shouldn't be a problem. However, if the integers are between 0 and 2^32 -1 (the range of general integers), you're not going to have enough memory to make an array that big. This answer would still be technically right, but I doubt a program that needs an array 4 GB large would be considered… [cont.] Answered by aaron - Sun Dec 7 04:12:31 2008 The sum of the squares of two consecutive odd integers is three less than eleven times the larger.?
Q. I consider myself pretty good at math but apparently I'm missing something here. An explanation would be nice! Thanks guys! The sum of the squares of two consecutive odd integers is three less than eleven times the larger. Find the two integers. Asked by Stefanie - Mon Apr 20 17:59:03 2009 - - 2 Answers - 0 Comments A. 5 and 7 (only 48 minutes too late!!) Answered by LaLa - Mon Apr 20 20:26:52 2009 From Yahoo Answer Search: "Integers"
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