Tanda (matematika): Perbedaan antara revisi

{{for|symbols named "… sign"|Daftar simbol matematika}}

 

'''Tanda''' dalam [[matematika]] merupakan suatu konsep yang berasal dari sifat setiap [[bilangan real]] yang bukan [[nol]] yang dapat berupa [[positif]] atau [[negatif]]. Bilangan [[0 (angka)|nol]] sendiri tidak bertanda, meskpun pada sejumlah konteks diperlukan juga suatu bilangan nol bertanda. Dalam penerapannya pada bilangan-bilangan real, "perubahan tanda" banyak digunakan dalam [[matematika]] dan [[fisika]] untuk menyatakan [[invers aditif]] ([[perkalian]] dengan bilangan [[−1]]), bahkan untuk kuantitas-kuantitas yang bukan bilangan real (yaitu yang tidak digolongkan atas positif, negatif atau nol). Juga, kata "tanda" dapa mengindikasikan aspek-aspek obyek matematika yang mirip dengan positivitas dan negativitas, seperti [[:en:Parity of a permutation|tanda suatu permutatsi]]<!-- (see [[#Other meanings|below]])-->.

 

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.

 

 

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.

===Tanda untuk bilangan nol ===

Note that this definition is culturally determined. In France and Belgium, 0 is said to be both positive and negative. The positive resp. negative numbers without zero are said to be "strictly positive" resp. "strictly negative".

 

==={{anchor|non-negative and non-positive}} Terminology for signs===

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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.

 

 

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.

=== Tanda suatu perubahan ===

:<math>\Delta x = x_\text{final} - x_\text{initial}. \,</math>

 

=== Tanda arah ===

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:

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In contrast, real numbers are stored and manipulated as [[Floating point]] values. The floating point values are represented using three separate values, mantissa, exponent, and, sign. Given this separate sign bit, it is possible to represent both positive and negative zero. Most programming languages normally treat positive zero and negative zero as equivalent values, albeit, they provide means by which the distinction can be detected.