HISTORY
In 976 AD the Persian encyclopedist Muhammad ibn Ahmad al-Khwarizmi, in
his "Keys of the Sciences", remarked that if, in a calculation, no
number appears in the place of tens, then a little circle should be used
"to keep the rows". This circle was called صفر (ṣifr,
"empty") in Arabic language. That was the earliest mention of the
name ṣifr that eventually became zero.
As the decimal zero
and its new mathematics spread from the Arab world to Europe in the Middle Ages,
words derived from ṣifr and zephyrus came
to refer to calculation, as well as to privileged knowledge and secret codes.
According to Ifrah, "in thirteenth-century Paris, a 'worthless fellow' was
called a '... cifre en algorisme', i.e., an 'arithmetical nothing'."
From ṣifr also came French chiffre =
"digit", "figure", "number", chiffrer =
"to calculate or compute", chiffré = "encrypted". Today, the
word in Arabic is still ṣifr, and cognates of ṣifrare
common in the languages of Europe and southwest Asia.
There are different
words used for the number or concept of zero depending on the context. For the
simple notion of lacking, the words nothing and none are often used, while nought, naught and aught are archaic and poetic forms with the same meaning.
Several sports have specific words for zero, such as nil in football, love in tennis and a duck in
cricket. In British
English, it is often called oh in the context of telephone numbers.
Slang words for zero include zip, zilch, nada, scratch and
even duck
egg or goose
egg
The number 0 is the smallest non-negative integer.
The natural number following 0 is 1 and no
natural number precedes 0. The number 0 may or may not be considered a natural number,
but it is a whole number and hence a rational
number and a real number (as
well as an algebraic number and a complex
number).
The number 0 is neither positive nor negative and
appears in the middle of a number line.
It is neither a prime number nor a composite
number. It cannot be prime because it has aninfinite number
of factors and
cannot be composite because it cannot be expressed by multiplying prime numbers
(0 must always be one of the factors).[39] Zero
is, however, even(see parity of
zero).
The following are some basic (elementary) rules for
dealing with the number 0. These rules apply for any real or complex number x,
unless otherwise stated.
·
Addition: x +
0 = 0 + x = x. That is, 0 is an identity
element (or neutral element) with respect to addition.
·
Subtraction: x −
0 = x and 0 − x = −x.
·
Multiplication: x ·
0 = 0 · x = 0.
·
Division: 0⁄x =
0, for nonzero x. But x⁄0 is undefined, because 0 has no multiplicative inverse (no real
number multiplied by 0 produces 1), a consequence of the previous rule; see division by
zero.
·
Exponentiation: x0 = x/x =
1, except that the case x = 0 may be left undefined in some
contexts; see Zero to the zero power. For all positive real x,
0x = 0.
The expression 0⁄0,
which may be obtained in an attempt to determine the limit of an expression of
the form f(x)⁄g(x) as
a result of applying the lim operator independently to both operands
of the fraction, is a so-called "indeterminate form". That does not simply
mean that the limit sought is necessarily undefined; rather, it means that the
limit of f(x)⁄g(x),
if it exists, must be found by another method, such as l'Hôpital's rule.
The sum of 0 numbers is 0, and the product
of 0 numbers is 1. The factorial 0!
evaluates to 1
·
In propositional logic, 0 may be used to
denote the truth value false.
In abstract algebra, 0 is commonly used to denote a zero
element, which is a neutral element for addition
·
In lattice
theory, 0 may denote the bottom
element of a bounded
lattice.
·
In recursion
theory, 0 can be used to denote the Turing degree of
the partial computable functions.
No comments:
Post a Comment