Second Stage: Developing a workable number system came next -- a system that had facilities for addition and subtraction to begin with, which would eventually offer facilities for multiplication and division also, for no arithmetic is plete without these four operations. What is more Devin Harris Womens Jersey , no other branch of mathematics could develop unless this bare minimum attained maturity. The precise origin of the second stage is lost in antiquity, but it seems that a workable number system developed simultaneously in several places around the world. Of these, the so-called Roman and the Arabic system are with us even today. Not all systems, obviously were equally efficient or intuitive and it can be illustrated by multiplying 25 with 25 in the two systems that are left with us. In the Roman system this would be (XXV)(XXV) whereas in the Arabic system it would be (25)(25). The first one would require several steps to solve, and in most case it would involve cumbersome numbers. On the other system, the Arabic multiplication would only involve multiplication of 25 by 5 first and by 2 after and a simple addition of these two. The invention of the abacus added to the ease of using the Arabic number system. What is more, the invention of the Arabic numbers, coupled with the invention of the number zero made it a powerful system for number-manipulation, and code-manipulation by implication. Plain geometry and algebra developed to a high level, making it possible to take coding to the next level where a single code-element such as x could now stand for ANY code whatsoever, the value of which is unknown till the code is decoded. Geometry depends upon numerous theorems. Each theorem represents something that would happen in the real world of circles, triangles, and rectangle. However Brandan Wright Womens Jersey , this information could be derived (or proved) only because these entities, otherwise physically drawn or constructed, could now be represented in terms of code that is susceptible to logical analysis. Third Stage: The decimal fraction (as opposed to the decimal number system, or the Arabic number system) developed about a millennia ago and it gave a big boost to the manipulation of fractions. An unusual level of precision came into mathematics for the first time, which in turn resulted in high levels of accuracy in code-manipulation. This in turn led to the discovery of Logarithms, where multiplication and division of large quantities was reduced to simple arithmetic of addition and subtraction, and that also of very small numbers. This moved plex code manipulation to simpler realms, making it possible to study the real world more easily through coded information. Soon it was found that numerous natural processes, say the perception of sound intensity by people, follow a logarithmic pattern or scale.
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