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[[File:PlusMinus.svg|thumb|right|150px|The [[plus and minus signs|plus and minus symbols]] are used to show the sign of a number.]]
{{distinguish2|the [[sine|sine function]] in trigonometry}}
{{for|symbols named "… sign"|table of mathematical symbols}}
 
In [[mathematics]], the concept of '''sign''' originates from the property of every non-zero [[real number]] to be positive or [[negative number|negative]]. [[0 (number)|Zero]] itself is signless, although in some contexts it makes sense to consider a [[signed zero]]. Along its application to real numbers, "change of sign" is used throughout mathematics and [[physics]] to denote the [[additive inverse]] (multiplication to [[−1]]), even for quantities which are not real numbers (so, which are not prescribed to be either positive, negative, or zero). Also, the word "sign" can indicate aspects of mathematical objects that resemble positivity and negativity, such as the [[Parity of a permutation|sign of a permutation]] (see [[#Other meanings|below]]).
 
==Sign of a number==
A [[real number]] is said to be positive if it is [[inequality (mathematics)|greater than]] zero, and [[negative number|negative]] if it is less than zero.  The attribute of being positive or negative is called the '''sign''' of the number.  Zero itself is not considered to have a sign.  Also, signs are not defined for [[complex numbers]], although the [[argument (complex analysis)|argument]] generalizes it in some sense.
 
In common [[numeral system|numeral notation]] (which is used in [[arithmetic]] and elsewhere), the sign of a number is often denoted by placing [[plus and minus signs|a plus sign or a minus sign]] before the number.  For example, +3 would denote a positive 3, and −3 would denote a negative 3.  When no plus or minus sign is given, the default interpretation is that a number is positive. Because of this notation, as well as the definition of negative numbers through [[subtraction]], the [[minus sign]] is perceived to have a strong association with negative numbers (of the negative sign). Likewise, "+" associates with positivity.
 
In [[algebra]], a minus sign is usually thought of as representing the operation of [[additive inverse]] (sometimes called ''negation''), with the additive inverse of a positive number being negative and the additive inverse of a negative number being positive.  In this context, it makes sense to write −(−3)&nbsp;=&nbsp;+3.
 
Any non-zero number can be changed to a positive one using the [[absolute value]] function.  For example, the absolute value of −3 and the absolute value of 3 are both equal to 3.  In symbols, this would be written |−3| = 3 and |3| = 3.
 
===Sign of zero===
The number [[0 (number)|zero]] is neither positive nor negative, and therefore has no sign.  In arithmetic, +0 and −0 both denote the same number 0, which is the additive inverse of itself.
 
In some contexts, such as [[signed number representations]] in [[computing]], it makes sense to consider signed versions of zero, with positive zero and negative zero being different numbers (see [[signed zero]]).
 
One also sees +0 and −0 in [[calculus]] and [[mathematical analysis]] when evaluating [[one-sided limit]]s. This notation refers to the behaviour of a function as the input variable approaches 0 from positive or negative values respectively; these behaviours are not necessarily the same.
 
==={{anchor|non-negative and non-positive}} Terminology for signs===
<!-- Several articles link to the above anchor -->
Because zero is neither positive nor negative, the following phrases are sometimes used to refer to the sign of an unknown number:
* A number is '''positive''' if it is greater than zero.
* A number is '''negative''' if it is less than zero.
* A number is '''non-negative''' if it is greater than or equal to zero.
* A number is '''non-positive''' if it is less than or equal to zero.
Thus a non-negative number is either positive or zero, while a non-positive number is either negative or zero.  For example, the [[absolute value]] of a real number is always non-negative, but is not necessarily positive.
 
The same terminology is sometimes used for [[Function (mathematics)|functions]] that take real or integer values.  For example, a function would be called positive if all of its values are positive, or non-negative if all of its values are non-negative.
 
===Sign convention===
{{main|Sign convention}}
In many contexts the choice of sign convention (which range of values is considered positive and which negative) is natural, whereas in others the choice is arbitrary subject only to consistency, the latter necessitating an explicit sign convention.
 
==Sign function==
[[Image:Signum function.svg|thumb|200px|Signum function ''y'' = sgn(''x'')]]
{{main|Sign function}}
The '''sign function''' or '''signum function''' is sometimes used to extract the sign of a number.  This function is usually defined as follows:
:<math> \sgn(x) = \begin{cases}
-1 & \text{if } x < 0, \\
~~\, 0 & \text{if } x = 0, \\
~~\, 1 & \text{if } x > 0. \end{cases}</math>
Thus sgn(''x'') is 1 when ''x'' is positive, and sgn(''x'') is −1 when ''x'' is negative.  For nonzero values of ''x'', this function can also be defined by the formula
:<math> \sgn(x) = \frac{x}{|x|}</math>
where |''x''| is the [[absolute value]] of ''x''.
 
==Meanings of sign==
===Sign of an angle===
[[File:Yhvyvczsa7.png|right|thumb|Measuring from the [[x-axis]], angles on the [[unit circle]] count as positive in the [[counterclockwise]] direction, and negative in the [[clockwise]] direction.]]
In many contexts, it is common to associate a sign with the measure of an [[angle]], particularly an oriented angle or an angle of [[rotation]].  In such a situation, the sign indicates whether the angle is in the [[clockwise]] or counterclockwise direction.  Though different conventions can be used, it is common in [[mathematics]] to have counterclockwise angles count as positive, and clockwise angles count as negative.
 
It is also possible to associate a sign to an angle of rotation in three dimensions, assuming the [[axis of rotation]] has been oriented. Specifically, a [[right-hand rule|right-handed]] rotation around an oriented axis typically counts as positive, while a left-handed rotation counts as negative.
 
===Sign of a change===
When a quantity ''x'' changes over time, the [[Finite difference|change]] in the value of ''x'' is typically defined by the equation
 
:<math>\Delta x = x_\text{final} - x_\text{initial}. \,</math>
 
Using this convention, an increase in ''x'' counts as positive change, while a decrease of ''x'' counts as negative change.  In [[calculus]], this same convention is used in the definition of the [[derivative]].  As a result, any [[Monotonic function|increasing function]] has positive derivative, while a decreasing function has negative derivative.
 
===Sign of a direction===
In [[analytic geometry]] and [[physics]], it is common to label certain directions as positive or negative.  For a basic example, the [[number line]] is usually drawn with positive numbers to the right, and negative numbers to the left:
[[File:Number-line.svg|center|600px]]
As a result, when discussing [[linear motion]], [[Displacement (vector)|displacement]] or [[velocity]] to the right is usually thought of as being positive, while similar motion to the left is thought of as being negative.
 
On the [[Cartesian plane]], the rightward and upward directions are usually thought of as positive, with rightward being the positive ''x''-direction, and upward being the positive ''y''-direction.  If a displacement or velocity [[Euclidean vector|vector]] is separated into its [[vector component]]s, then the horizontal part will be positive for motion to the right and negative for motion to the left, while the vertical part will be positive for motion upward and negative for motion downward.
 
===Signedness in computing===
<div class="thumb tright"><div style="width:20em;">
{|style="width:100%; margin:0;" cellspacing="0"
|align="center" style="background-color:#ddeeff;"| [[Most significant bit|most-significant bit]] ||align="center" colspan="9"|
|-
|align="center" style="width:2em; background-color:#ddeeff; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-left:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-right:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em;"| '''=''' ||align="right" style="width:2em;"| '''127'''
|-
|align="center" style="width:2em; background-color:#ddeeff; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-left:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-right:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em;"| '''=''' ||align="right" style="width:2em;"| '''126'''
|-
|align="center" style="width:2em; background-color:#ddeeff; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-left:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-right:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em;"| '''=''' ||align="right" style="width:2em;"| '''2'''
|-
|align="center" style="width:2em; background-color:#ddeeff; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-left:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-right:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em;"| '''=''' ||align="right" style="width:2em;"| '''1'''
|-
|align="center" style="width:2em; background-color:#ddeeff; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-left:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-right:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em;"| '''=''' ||align="right" style="width:2em;"| '''0'''
|-
|align="center" style="width:2em; background-color:#ddeeff; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-left:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-right:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em;"| '''=''' ||align="right" style="width:2em;"| '''&minus;1'''
|-
|align="center" style="width:2em; background-color:#ddeeff; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-left:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-right:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em;"| '''=''' ||align="right" style="width:2em;"| '''&minus;2'''
|-
|align="center" style="width:2em; background-color:#ddeeff; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-left:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-right:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em;"| '''=''' ||align="right" style="width:2em;"| '''&minus;127'''
|-
|align="center" style="width:2em; background-color:#ddeeff; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-left:1px solid #aaaaaa;"| '''1'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em; border-top:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa; border-right:1px solid #aaaaaa;"| '''0'''
|align="center" style="width:2em;"| '''=''' ||align="right" style="width:2em;"| '''&minus;128'''
|}
{{caption|Most computers use [[two's complement]] to represent the sign of an integer.}}
</div></div>
{{main|Signedness}}
In [[computing]], a numeric value may be either signed or unsigned, depending on whether the computer is keeping track of a sign for the number. By restricting a [[Variable (programming)|variable]] to non-negative values only, one more [[bit]] can be used for storing the value of a number.
 
Because of the way arithmetic is done within computers, the sign of a signed variable is usually not stored as a single independent bit, but is instead stored using [[two's complement]] or some other [[signed number representation]].
 
===Other meanings===
[[File:VFPt_dipole_electric.svg|thumb|right|[[Electric charge]] may be positive or negative.]]
In addition to the sign of a real number, the word sign is also used in various related ways throughout mathematics and the sciences:
* Words ''[[up to]] sign'' mean that for a quantity {{mvar|q}} is known that either {{math|1=''q'' = ''Q''}} or {{math|1=''q'' = −''Q''}} for certain {{mvar|Q}}. In is often expressed as {{math|1=''q'' = [[±]]''Q''}}. For real numbers, it means that only the [[absolute value]] {{math|{{!}}''q''{{!}}}} of the quantity is known. For [[complex numbers]] and [[vector space|vectors]], a quantity known up to sign is a stronger condition than a quantity with known [[norm (mathematics)|magnitude]]: aside {{mvar|Q}} and {{math|−''Q''}}, there are many other possible values of {{mvar|q}} such that {{math|1={{!}}''q''{{!}} = {{!}}''Q''{{!}}}}.
* The [[Parity of a permutation|sign of a permutation]] is defined to be positive if the permutation is even, and negative if the permutation is odd.
* In [[graph theory]], a [[signed graph]] is a graph in which each edge has been marked with a positive or negative sign.
* In [[mathematical analysis]], a [[signed measure]] is a generalization of the concept of [[measure (mathematics)|measure]] in which the measure of a set may have positive or negative values.
* In a [[signed-digit representation]], each digit of a number may have a positive or negative sign.
* The ideas of [[signed area]] and [[signed volume]] are sometimes used when it is convenient for certain areas or volumes to count as negative.  This is particularly true in the theory of [[determinant]]s.
* In [[physics]], any [[electric charge]] comes with a sign, either positive or negative.  By convention, a positive charge is a charge with the same sign as that of a [[proton]], and a negative charge is a charge with the same sign as that of an [[electron]].
 
== See also ==
* [[Positive element]]
* [[Symmetry in mathematics]]
 
[[Category:Elementary arithmetic]]
[[Category:Numbers]]
[[Category:Mathematical terminology]]

Revision as of 18:53, 14 January 2014

The plus and minus symbols are used to show the sign of a number.

Template:Distinguish2 28 year-old Painting Investments Worker Truman from Regina, usually spends time with pastimes for instance interior design, property developers in new launch ec Singapore and writing. Last month just traveled to City of the Renaissance.

In mathematics, the concept of sign originates from the property of every non-zero real number to be positive or negative. Zero itself is signless, although in some contexts it makes sense to consider a signed zero. Along its application to real numbers, "change of sign" is used throughout mathematics and physics to denote the additive inverse (multiplication to −1), even for quantities which are not real numbers (so, which are not prescribed to be either positive, negative, or zero). Also, the word "sign" can indicate aspects of mathematical objects that resemble positivity and negativity, such as the sign of a permutation (see below).

Sign of a number

A real number is said to be positive if it is greater than zero, and negative if it is less than zero. The attribute of being positive or negative is called the sign of the number. Zero itself is not considered to have a sign. Also, signs are not defined for complex numbers, although the argument generalizes it in some sense.

In common numeral notation (which is used in arithmetic and elsewhere), the sign of a number is often denoted by placing a plus sign or a minus sign before the number. For example, +3 would denote a positive 3, and −3 would denote a negative 3. When no plus or minus sign is given, the default interpretation is that a number is positive. Because of this notation, as well as the definition of negative numbers through subtraction, the minus sign is perceived to have a strong association with negative numbers (of the negative sign). Likewise, "+" associates with positivity.

In algebra, a minus sign is usually thought of as representing the operation of additive inverse (sometimes called negation), with the additive inverse of a positive number being negative and the additive inverse of a negative number being positive. In this context, it makes sense to write −(−3) = +3.

Any non-zero number can be changed to a positive one using the absolute value function. For example, the absolute value of −3 and the absolute value of 3 are both equal to 3. In symbols, this would be written |−3| = 3 and |3| = 3.

Sign of zero

The number zero is neither positive nor negative, and therefore has no sign. In arithmetic, +0 and −0 both denote the same number 0, which is the additive inverse of itself.

In some contexts, such as signed number representations in computing, it makes sense to consider signed versions of zero, with positive zero and negative zero being different numbers (see signed zero).

One also sees +0 and −0 in calculus and mathematical analysis when evaluating one-sided limits. This notation refers to the behaviour of a function as the input variable approaches 0 from positive or negative values respectively; these behaviours are not necessarily the same.

<non-negative and non-positive>...</non-negative and non-positive> Terminology for signs

Because zero is neither positive nor negative, the following phrases are sometimes used to refer to the sign of an unknown number:

  • A number is positive if it is greater than zero.
  • A number is negative if it is less than zero.
  • A number is non-negative if it is greater than or equal to zero.
  • A number is non-positive if it is less than or equal to zero.

Thus a non-negative number is either positive or zero, while a non-positive number is either negative or zero. For example, the absolute value of a real number is always non-negative, but is not necessarily positive.

The same terminology is sometimes used for functions that take real or integer values. For example, a function would be called positive if all of its values are positive, or non-negative if all of its values are non-negative.

Sign convention

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. In many contexts the choice of sign convention (which range of values is considered positive and which negative) is natural, whereas in others the choice is arbitrary subject only to consistency, the latter necessitating an explicit sign convention.

Sign function

Signum function y = sgn(x)

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. The sign function or signum function is sometimes used to extract the sign of a number. This function is usually defined as follows:

sgn(x)={1if x<0,0if x=0,1if x>0.

Thus sgn(x) is 1 when x is positive, and sgn(x) is −1 when x is negative. For nonzero values of x, this function can also be defined by the formula

sgn(x)=x|x|

where |x| is the absolute value of x.

Meanings of sign

Sign of an angle

Measuring from the x-axis, angles on the unit circle count as positive in the counterclockwise direction, and negative in the clockwise direction.

In many contexts, it is common to associate a sign with the measure of an angle, particularly an oriented angle or an angle of rotation. In such a situation, the sign indicates whether the angle is in the clockwise or counterclockwise direction. Though different conventions can be used, it is common in mathematics to have counterclockwise angles count as positive, and clockwise angles count as negative.

It is also possible to associate a sign to an angle of rotation in three dimensions, assuming the axis of rotation has been oriented. Specifically, a right-handed rotation around an oriented axis typically counts as positive, while a left-handed rotation counts as negative.

Sign of a change

When a quantity x changes over time, the change in the value of x is typically defined by the equation

Δx=xfinalxinitial.

Using this convention, an increase in x counts as positive change, while a decrease of x counts as negative change. In calculus, this same convention is used in the definition of the derivative. As a result, any increasing function has positive derivative, while a decreasing function has negative derivative.

Sign of a direction

In analytic geometry and physics, it is common to label certain directions as positive or negative. For a basic example, the number line is usually drawn with positive numbers to the right, and negative numbers to the left:

As a result, when discussing linear motion, displacement or velocity to the right is usually thought of as being positive, while similar motion to the left is thought of as being negative.

On the Cartesian plane, the rightward and upward directions are usually thought of as positive, with rightward being the positive x-direction, and upward being the positive y-direction. If a displacement or velocity vector is separated into its vector components, then the horizontal part will be positive for motion to the right and negative for motion to the left, while the vertical part will be positive for motion upward and negative for motion downward.

Signedness in computing

most-significant bit
0 1 1 1 1 1 1 1 = 127
0 1 1 1 1 1 1 0 = 126
0 0 0 0 0 0 1 0 = 2
0 0 0 0 0 0 0 1 = 1
0 0 0 0 0 0 0 0 = 0
1 1 1 1 1 1 1 1 = −1
1 1 1 1 1 1 1 0 = −2
1 0 0 0 0 0 0 1 = −127
1 0 0 0 0 0 0 0 = −128

Template:Caption

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. In computing, a numeric value may be either signed or unsigned, depending on whether the computer is keeping track of a sign for the number. By restricting a variable to non-negative values only, one more bit can be used for storing the value of a number.

Because of the way arithmetic is done within computers, the sign of a signed variable is usually not stored as a single independent bit, but is instead stored using two's complement or some other signed number representation.

Other meanings

Electric charge may be positive or negative.

In addition to the sign of a real number, the word sign is also used in various related ways throughout mathematics and the sciences:

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    A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

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    A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

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    A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

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    This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

    A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

    If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

    Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer..
  • The sign of a permutation is defined to be positive if the permutation is even, and negative if the permutation is odd.
  • In graph theory, a signed graph is a graph in which each edge has been marked with a positive or negative sign.
  • In mathematical analysis, a signed measure is a generalization of the concept of measure in which the measure of a set may have positive or negative values.
  • In a signed-digit representation, each digit of a number may have a positive or negative sign.
  • The ideas of signed area and signed volume are sometimes used when it is convenient for certain areas or volumes to count as negative. This is particularly true in the theory of determinants.
  • In physics, any electric charge comes with a sign, either positive or negative. By convention, a positive charge is a charge with the same sign as that of a proton, and a negative charge is a charge with the same sign as that of an electron.

See also