The first thing to say about zero is that there are two uses of zero which are both extremely important but are somewhat different. One use is as an empty place indicator in our place-value number system. Hence in a number like 2106 the zero is used so that the positions of the 2 and 1 are correct. Clearly 216 means something quite different. The second use of zero is as a number itself in the form we use it as 0. There are also different aspects of zero within these two uses, namely the concept, the notation, and the name.
... the mathematical conception of zero ... was also present in the spiritual form from 17 000 years back in India.
The nr. zero was invented independently in India and by the Maya. In India a decimal system was used, like ours, but they used an empty space for zero up to 3rd Century BC. This was confusing for an empty space was also used to separate numbers, and so they invented the dot for a zero. The first evidence for the use of the symbol that we now know as zero stems from the 7th century AD. The Maya invented the number zero for their calendars in the 3rd century AD. The number zero reached European civilisation through the Arabs after 800 AD. The Greek and Roman did not need the number zero for they did their calculations on an abacus. The name 'zero' comes from the arabic 'sifr'.
In around 500AD Aryabhata devised a number system which has no zero yet was a positional system. He used the word "kha" for position and it would be used later as the name for zero. There is evidence that a dot had been used in earlier Indian manuscripts to denote an empty place in positional notation. It is interesting that the same documents sometimes also used a dot to denote an unknown where we might use x. Later Indian mathematicians had names for zero in positional numbers yet had no symbol for it. The first record of the Indian use of zero which is dated and agreed by all to be genuine was written in 876. We are usually taught to count "one to ten" first. Then, we are told that zero is a placeholder. After that we learn that it is equal to nothing. In this article, you'll learn a much easier way to understand the concept of zero.
(1) A quantity divided by zero becomes a fraction the denominator of which is zero. This fraction is termed an infinite quantity. In this quantity consisting of that which has zero for its divisor, there is no alteration, though many may be inserted or extracted; as no change takes place in the infinite and immutable God when worlds are created or destroyed, though numerous orders of beings are absorbed or put forth.
(2) If we subtract a positive number from zero the same negative number remains. ... if we subtract a negative number from zero the same positive number remains.
The concept of Zero is attributed to the Hindus. The Hindus were also the first to use zero in the way it is used today. Some symbol was required in positional number systems to mark the place of a power of the base not actually occurring. This was indicated by the Hindus by a small circle, which was called Shunya, the Sanskrit word for vacant. This was translated into the Arabic Sifr about 800 A.D. Subsequent changes have given us the word zero.
The sum of zero and a negative number is negative, the sum of a positive number and zero is positive, the sum of zero and zero is zero. Quipu, a knotted cord device, used in the Inca Empire and its predecessor societies in the Andeanregion to record accounting and other digital data, is encoded in a base ten positional system. Zero is represented by the absence of a knot in the appropriate position. The renowned mathematicians among the Ancient Greeks, who learned the fundamentals of their math from the Egyptians, did not have a name for zero, nor did their system feature a placeholder as did the Babylonian. They may have pondered it, but there is no conclusive evidence to say the symbol even existed in their language. It was the Indians who began to understand zero both as a symbol and as an idea. The Italian mathematician, Fibonacci, built on Al-Khowarizmi's work with algorithms in his book Liber Abaci, or "Abacus book," in 1202. Until that time, the abacus had been the most prevalent tool to perform arithmetic operations. Fibonacci's developments quickly gained notice by Italian merchants and German bankers, especially the use of zero. Accountants knew their books were balanced when the positive and negative amounts of their assets and liabilities equaled zero. But governments were still suspicious of Arabic numerals because of the ease in which it was possible to change one symbol into another. Though outlawed, merchants continued to use zero in encrypted messages, thus the derivation of the word cipher, meaning code, from the Arabic sifr. The second appearance of zero occurred independently in the New World, in Mayan culture, likely in the first few centuries A.D. "That, I suppose, is the most striking example of the zero being devised wholly from scratch," Kaplan says. Kaplan pinpoints an even earlier emergence of a placeholder zero, a pair of angled wedges used by the Sumerians to denote an empty number column some 4,000 to 5,000 years ago. Zero has played quite a role in making of numerals or at least modern numerals. The modern numerals were based on the Arabic numeric system as indicated by this article. Al-Khw rizm+ laid foundation to modern numerics in Arabic format of course. Not to forget he is the same guy who laid foundation of Algebra and Algorithms to name a a few.
IMPORTANCE OF ZERO: Before you talk about existence or non-existence of zero would you care to explain what mathematical objects you think do exist and in what sense. Moreover, why are these other things you trust not also inventions "just to make stuff work"? | |
if i have an apple i name the quantity 1... so if i have two apples i can i can do 1*2 and get 2 apples... so in that sense 1 exists.... but saying that you have 0 apples when you have nothing is not the same thing... because 0 is nothing... | |
One might have thought that the progress of the number systems in general, and zero in particular, would have been steady from this time on. However, this was far from the case. Cardan solved cubic and quartic equations without using zero. He would have found his work in the 1500's so much easier if he had had a zero but it was not part of his mathematics. By the 1600's zero began to come into widespread use but still only after encountering a lot of resistance. Zero,(that is ,the '0'symbol in mathematics) is really a wonderful invention by our anicients.A heap of objects however large can be counted easily by deviding them into groups of ten objects. Again ten such groups, each containing ten objects, can be sealed into a bag to contain one hundred objects .Ten such bags can be put into a bigger bag which then contains 1000 objects.
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