# Essay about Number System in Mathematics

2773 Words Apr 21st, 2011 12 Pages
Introduction I. Number Systems in Mathematics:
A Number system (or system of numeration) is a writing system for expressing numbers, that is a mathematical notation for representing number of a given set, using graphemes or symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases.
Ideally, a number system will: * Represent a useful set of numbers (e.g. all integers, or rational numbers) * Give every number represented a unique representation (or at least a standard representation) * Reflect the algebraic and arithmetic structure of the numbers.
For example,
The word “decimal” describes a system that has ten possible digits. These are the digits 0 through 9. Every number expressed in the decimal system is a combination of these ten digits. You use the decimal system every day, it comes naturally, we all have 10 fingers and 10 toes (unless your family tree doesn’t fork, but let’s not go there), and some of us use those 10 fingers and toes extensively to help with every day addition and subtraction.
The binary system works essentially the same way, with the only difference that it only has two digits. These are visually expressed by the digits 0 and 1. Every number expressed in the binary system is a combination of these two digits. b. History
The Indian scholar Pingala (circa 5th–2nd centuries BC) developed mathematical concepts for describing prosody, and in so doing presented the first known description of a binary numeral system. He used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), making it similar to Morse code. In the 11th century, scholar and philosopher Shao Yong developed a method for arranging the hexagrams which corresponds to the sequence 0 to 63, as represented in binary, with yin as 0, yang as 1 and the least significant bit on top.
Similar sets of binary combinations have also been used in traditional African divination systems such as Ifá as well as in

## Related Documents

• ###### Essay Mathematics And The Basic Fundamentals Of Mathematics

One’s entire perception of Mathematics lies afar from the precise and relevant information contained with one of the extensive subjects in the world today. Mathematics as a formal area of teaching and learning was developed about 5,000 years ago by the Sumerians. To correctly define Mathematics is as difficult as attempting to lay a finger upon the sun, contemplating an idea as to how to contain all Mathematics withholds into one simple sentence accurately is unmanageable. However, when attempted…

Words: 1371 - Pages: 6
• ###### Essay The First Invention Of Mathematics

Abstract: This paper reveals the birth of mathematics. Representing quantities in some way is considered the first invention of mathematics. We use mathematics every day in one way or another. Sometimes we even use mathematics unconsciously, as in the case of filing a cup of water for cooking. The measure cup is readily available to us and all we have to do is fill it out, but who started this type of measurement? How old is mathematics? Specifically, how old is counting? When was representing quantities…

Words: 1929 - Pages: 8
• ###### Scope of Mathematics Essay

Scope of mathematics This article will provide an overview of the NCTM process and content standards. Educators first studying the standards may feel overwhelmed with the amount of content addressed within each grade-level span. State frameworks that dictate standards for each grade level exacerbate this situation. However, a longitudinal view will show how the same topics are developed over several years in a spiral and interconnected pattern. For example, the…

Words: 3626 - Pages: 15
• ###### Essay Is Mathematics Invented Or Discovered?

Leopold Kronecker stated that: ‘God made the integers, all else is the work of man’, discuss this statement and use it as a starting point to answer the question; is Mathematics invented or discovered? Mathematics is certainly the most intriguing and unusual science, not just because it uses abstract concepts to describe the physical world but also because it is the root of all the sciences; without it physics would most certainly be redundant. It is especially unusual as it concerns a subject that…

Words: 1539 - Pages: 7
• ###### Essay Applications of Discrete Mathematics

DISCRETE MATHEMATICS Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects…

Words: 2040 - Pages: 9
• ###### The History of Math Essay

science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems. The basic of mathematics was inherited by the Greeks and independent by the Greeks beg the major Greek progress in mathematics was from 300 BC to 200 AD. After…

Words: 814 - Pages: 4
• ###### Mth 110 Essay examples

The Influence of Mathematics on Daily Social Activities MTH/110 March 2, 2015 The Influence of Mathematics Society is an important concept in which stands the intellectual development of mathematics and science. Today, in society, mathematics makes extraordinary demands and so to the world of mathematicians and scientists. The purpose of the report is to identify the influence and effects of mathematics in society. It includes some history of math and its major demands…

Words: 1427 - Pages: 6
• ###### Essay Evolution Of Zero Throughout History

ancient Mesopotamian mathematics to modern day mathematics. Understanding the concept of zero and learning to work with it is the basis of our world today. If zero did not exist then we would not have calculus, financial accounting, and the ability to make simple arithmetic calculations. The idea of zero has crossed the imagination of great minds across the globe. Zero functions as a placeholder and the amount of zeroes after a digit can drastically change the value of the number just imagine if one…

Words: 2496 - Pages:
• ###### Essay Mathematics And The Language Of Mathematics

When it comes to the subject of mathematics, the challenge in teaching kids not only lies within learning the concepts, but also in learning the vocabulary of mathematics which describe these concepts. Mathematics incorporates theory and formula in order to produce answers. It is these answers that have agreed upon labels in the form of vocabulary. When students begin the process of learning mathematics through formulas, it is imperative that they begin learning the vocabulary necessary to communicate…

Words: 1172 - Pages: 5
• ###### The Number Line Essay

SCIENCES MATHEMATICS DEPARTMENT RESEARCH SEMINAR IN MATHEMATICS MATH 4460 01 THE NUMBER LINE BY George L Williams III Contents * THE NUMBER LINE * Extended real number line * Drawing the number line * Line segmentation * Comparing numbers * Arithmetic Operations * Arithmetic Operations (cont.) * Algebraic properties * Cartesian Plane/Cartesian Coordinate System * An Overview * My words * Applications of the number line…

Words: 3861 - Pages: 16