Tuesday, March 27, 2018

MATHEMATICA 1






1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph. It represents a single entity, the unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. It is also the first of the infinite sequence of natural numbers, followed by 2.


It is also the first and second number in the Fibonacci sequence (0 is the zeroth) and is the first number in many other mathematical sequences.

1 is neither a prime number nor a composite number, but a unit (meaning of ring theory), like −1 and, in the Gaussian integers, i and −i. The fundamental theorem of arithmetic guarantees unique factorization over the integers only up to units. (For example, 4 = 22, but if units are included, is also equal to, say, (−1)6 × 123 × 22, among infinitely many similar "factorizations".)

1 is the only positive integer divisible by exactly one positive integer (whereas prime numbers are divisible by exactly two positive integers, composite numbers are divisible by more than two positive integers, and zero is divisible by all positive integers). 1 was formerly considered prime by some mathematicians, using the definition that a prime is divisible only by 1 and itself. However, this complicates the fundamental theorem of arithmetic, so modern definitions exclude units.

1 is the atomic number of hydrogen.

In the philosophy of Plotinus and a number of other neoplatonists, The One is the ultimate reality and source of all existence. Philo of Alexandria (20 BC – AD 50) regarded the number one as God's number, and the basis for all numbers ("De Allegoriis Legum," ii.12 [i.66]).


The Express - Concerning One

1. The ancient Greeks did not consider One to be a number at all. A number, said Euclid, is an “aggregate of units”, so numbers began at Two.

2. They also considered One to be both male and female and both odd and even.

3. There is only one hiccup in the works of Shakespeare, uttered, appropriately enough, by Sir Toby Belch in Twelfth Night.

4. The Icelandic for “one” is “eitt”, which sounds just like “eight”.

5. Each hair on a human head grows one centimetre a month.

6. The word “girl” only occurs once in the King James Bible (in Joel 3:3). The King James Bible, incidentally, was first published on May 2, 1611.

7. In the UK, a first wedding anniversary is a cotton anniversary; in the USA it is paper.

8. Among the words Charles Dickens used only once are “kangaroo” (in David Copperfield) and “zoo” (in Martin Chuzzlewit).

9. A word that any particular author used only once in their works is called a “hapax legomenon”.

10. “One” is the 35th most commonly used word in the English language, just ahead of “all”.


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