Symbols:Prime
Prime
- $x^\prime$
The prime symbol $'$ is a general indicator of another version of or another type of where the specific version or type that is being described is to be defined.
The symbol $x'$ should technically be voiced x prime, although colloquially referred to as some variant of x dash or x tick or whatever can be devised by the ingenuity of the reader.
The prime symbol can be repeated: $x' '$ and $x' ' '$, and so on, to indicate a further variation of the type of $x$, according to the appropriate definition.
The $\LaTeX$ code for \(x'\) is x' or x^\prime.
The $\LaTeX$ code for \(x' '\) is x' ' or x^{\prime \prime}.
The $\LaTeX$ code for \(x' ' '\) is x' ' ' or x^{\prime \prime \prime}.
Usage
Feet and Inches
- ${}^\prime$ and ${}^{\prime \prime}$
One of the symbols in general use for feet and inches is ${}^{\prime}$ and ${}^{\prime \prime}$.
Thus, for example, $6$ feet $3$ inches is presented as:
- $6^\prime \, 3^{\prime \prime}$
The $\LaTeX$ code for \(6^\prime \, 3^{\prime \prime}\) is 6^\prime \, 3^{\prime \prime} or 6' \, 3' '.
Minutes and Seconds
- ${}^\prime$ and ${}^{\prime \prime}$
The usual symbols in general use for minutes and seconds are ${}^{\prime}$ and ${}^{\prime \prime}$.
Thus, for example, an angle of $10$ degrees, $3$ minutes and $27$ seconds is presented as:
- $10 \degrees \, 3^\prime \, 27^{\prime \prime}$
The $\LaTeX$ code for \(10 \degrees \, 3^\prime \, 27^{\prime \prime}\) is 10 \degrees \, 3^\prime \, 27^{\prime \prime} or 10 \degrees \, 3' \, 27^' '.
Constant Value of Variable
- $\tuple {x^\prime, y^\prime}$
Often used to represent a constant value of a variable.
For example, let $\tuple {x, y}$ denote the Cartesian coordinates of a variable point in the plane describing the locus of a curve.
Then $\tuple {x', y'}$ can be used to denote an arbitrary constant point on that curve.
The $\LaTeX$ code for \(\tuple {x^\prime, y^\prime}\) is \tuple {x^\prime, y^\prime} or \tuple {x', y'}.
Related Variable
- $\tuple {x^\prime, y^\prime}$
Often used to represent a variable or constant which is related in some way to another previously declared variable or constant.
For example, let $\tuple {x, y}$ denote the Cartesian coordinates of a variable point in the plane.
Then $\tuple {x', y'}$ can be used to denote the same point in the plane after a transformation.
The $\LaTeX$ code for \(\tuple {x^\prime, y^\prime}\) is \tuple {x^\prime, y^\prime} or \tuple {x', y'}.
Derivative
- $\map {f^\prime} x$
Used to denote the derivative of a function.
Thus for a function $\map f x$:
- $\map {f^\prime} x$ denotes the first derivative of $\map f x$
- $\map {f^{\prime \prime} } x$ denotes the second derivative of $\map f x$
- $\map {f^{\prime \prime \prime} } x$ denotes the third derivative of $\map f x$.
For $n$ beyond $3$, it is usual to use the notation $\map {f^{\paren n} } x$ for the $n$th derivative of $\map f x$.
The $\LaTeX$ code for \(\map {f^\prime} x\) is \map {f^\prime} x or \map {f'} x.
The $\LaTeX$ code for \(\map {f^{\prime \prime} } x\) is \map {f^{\prime \prime} } x or \map {f' '} x.
The $\LaTeX$ code for \(\map {f^{\prime \prime \prime} } x\) is \map {f^{\prime \prime \prime} } x or \map {f' ' '} x.
Also known as
The prime symbol ${}^\prime$ is also known as the accent symbol.
Technical Note
Note that there are rendering issues with the prime symbol $'$ in the Mathjax version of $\LaTeX$.
Spaces need to be included between adjacent instances of $'$.
Otherwise, MathJax will interpret consecutive instances as compiler imperatives to implement italics or bold.
Hence, for example, the $\LaTeX$ for $x' '$ needs to be written as x' '.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): prime: 5.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): prime symbol (accent)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): prime symbol (accent)