For some quantities, the zero level is naturally distinguished from all other levels, whereas for others it is more or less arbitrarily chosen. For example, for an absolute temperature (typically measured in kelvins), zero is the lowest possible value. In physics, the zero-point energy is the lowest possible energy that a quantum mechanical physical system may possess and is the energy of the ground state of the system. Adding (or subtracting) 0 to any number leaves that number unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 results in 0, and consequently division by zero has no meaning in arithmetic.

Elementary algebra

A positive or negative number when divided by zero is a fraction with the zero as denominator. Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. While mathematicians all accept zero as a number, some non-mathematicians would say that zero is not a number, arguing that one cannot have zero of something. Others say that if one has a bank balance of zero, one has a specific quantity of money in that account, namely none. It is that latter view which is accepted by mathematicians and most others.

• In physics, the zero-point energy is the lowest possible energy that a quantum mechanical physical system may possess and is the energy of the ground state of the system.
• For some quantities, the zero level is naturally distinguished from all other levels, whereas for others it is more or less arbitrarily chosen.
• The modern numeral 0 is normally written as a circle or (rounded) rectangle.
• Multiplying any number by 0 results in 0, and consequently division by zero has no meaning in arithmetic.

Other uses in mathematics

A quantity divided by zero becomes a fraction the denominator of which is zero. However, those used in the United Kingdom do not make the letter o pin-up casino india and the number 0 look different from each other, because there can never be any mistake if the letters are correctly spaced. In paper writing, one does not have to make the 0 (zero) and O (letter O) look different at all. Or you may add a slash across the zero in order to show the difference.

• The following table includes all of the above examples along with other operations in a condensed, generalized form (where x represents any number).
• Others say that if one has a bank balance of zero, one has a specific quantity of money in that account, namely none.
• A positive or negative number when divided by zero is a fraction with the zero as denominator.
• The rule which has the letter O with a slash and the zero without was used at IBM and a few other early mainframe makers; this is even more of a problem for Scandinavians, because it looks like two of their letters at the same time.
• These representations include the signed magnitude and ones’ complement binary integer representations (but not the two’s complement binary form used in most modern computers), and most floating-point number representations (such as IEEE 754 and IBM S/360 floating-point formats).

Telling zero and the letter O apart

In mathematics, there is no “positive zero” or “negative zero” distinct from zero; both −0 and +0 represent exactly the same number. However, in some computer hardware signed number representations, zero has two distinct representations, a positive one grouped with the positive numbers and a negative one grouped with the negatives. This kind of dual representation is known as signed zero, with the latter form sometimes called negative zero. These representations include the signed magnitude and ones’ complement binary integer representations (but not the two’s complement binary form used in most modern computers), and most floating-point number representations (such as IEEE 754 and IBM S/360 floating-point formats).

The Arabic-language inheritance of science was largely Greek,61 followed by Hindu influences.62 In 773, at Al-Mansur’s behest, translations were made of many ancient treatises including Greek, Roman, Indian, and others.

In old-style fonts with text figures, 0 is usually the same height as a lowercase x. The rule which has the letter O with a slash and the zero without was used at IBM and a few other early mainframe makers; this is even more of a problem for Scandinavians, because it looks like two of their letters at the same time. Some Burroughs/Unisys computers display a zero with a backwards slash. The following table includes all of the above examples along with other operations in a condensed, generalized form (where x represents any number). Also in set theory, 0 is the lowest ordinal number, corresponding to the empty set viewed as a well-ordered set. In order theory (and especially its subfield lattice theory), 0 may denote the least element of a lattice or other partially ordered set.

The number 0 is the smallest nonnegative integer, and the largest nonpositive integer. The number 0 may or may not be considered a natural number,7172 but it is an integer, and hence a rational number and a real number.73 All rational numbers are algebraic numbers, including 0. When the real numbers are extended to form the complex numbers, 0 becomes the origin of the complex plane. The modern numeral 0 is normally written as a circle or (rounded) rectangle.