HOW DID THE ANCIENTS USE NUMBERS

1. HOW DID THE ANCIENTS USE NUMBERS

2. INTRODUCTION • In mathematics, zero, symbolized by the numeric character O, is both: 1. In a positional number system, a place indicator meaning "no units of this multiple." For example, in the decimal number 1,041, there is one unit in the thousands position, no units in the hundreds position, four units in the tens position, and one unit in the 1-9 position. • 2. An independent value midway between +1 and -1. In writing outside of mathematics, depending on the context, various denotative or connotative meanings for zero include "total failure," "absence," "nil," and "absolutely nothing." ("Nothing" is an even more abstract concept than "zero" and their meanings sometimes intersect.)

3. Historical Facts Zero is both a number and the numerical digit used to represent that number in numerals. It plays a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, zero is used as a placeholder in place value systems. In the English language, zero may also be called oh, null, nil or naught. O is the integer preceding 1. In most systems, 0 was identified before the idea of 'negative integers' was accepted. Zero is an even number. O is neither positive nor negative. Zero is a number which quantifies a count or an amount of null size; that is, if the number of your brothers is zero, that means the same thing as having no brothers, and if something has a weight of zero, it has no weight.

4. Historical Facts • If the difference between the number of pieces in two piles is zero, it means the two piles have an equal number of pieces. Before counting starts, the result can be assumed to be zero; that is the number of items counted before you count the first item and counting the first item brings the result to one. And if there are no items to be counted, zero remains the final result. The number zero as we know it arrived in Europe, most famously delivered by Italian mathematician Fibonacci (aka Leonardo of Pisa), who brought it, along with the rest of the Arabic numerals, back from his travels to north Africa. But the history of zero, both as a concept and a number, stretches far deeper into history.

5. Introduction To Europe • Records show that the ancient Greeks seemed unsure about the status of zero as a number. They asked themselves, "How can nothing be something?", leading to philosophical and, by the Medieval period, religious arguments about the nature and existence of zero and the vacuum. The paradoxes of Zeno of Elea depend in large part on the uncertain interpretation of zero. • Example of the early Greek symbol for zero (lower right corner) from a 2nd century papyrus • By 130 AD, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero (a small circle with a long overbar) within a sexagesimal numeral system otherwise using alphabetic Greek numerals.

6. Introduction To Europe • Because it was used alone, not just as a placeholder, this Hellenistic zero was perhaps the first documented use of a number zero in the Old World. However, the positions were usually limited to the fractional part of a number (called minutes, seconds, thirds, fourths, etc.)—they were not used for the integral part of a number. In later Byzantine manuscripts of Ptolemy's Syntaxis Mathematica (also known as the Almagest), the Hellenistic zero had morphed into the Greek letter omicron (otherwise meaning 70). • Another zero was used in tables alongside Roman numerals by 525 (first known use by Dionysius Exiguus), but as a word, nulla meaning "nothing", not as a symbol. When division produced zero as a remainder, nihil, also meaning "nothing", was used. These medieval zeros were used by all future medieval computes (calculators of Easter). The initial "N" was used as a zero symbol in a table of Roman numerals by Bede or his colleague around 725.

7. Expansion of Math • Zero expanded math and calculations because now we have a barrier between positive and negative numbers. Now we have place value and now we can create infinite value of number from just 9 digits.

8. Summary • Mathematics is all about quantities. Some, more, lots. Whatever. But we can only express those amounts as numbers, or mathematical statements, if we're able to compare it to "nothing"So therefore we need a way to express "nothing" in a way that fits in with our ways of expressing "something“. Which is why zero is probably the most important and the most amazing number ever invented.