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[8] [9] In programming languages such as Ada, [10] Fortran, [11] Perl, [12] Python [13] and Ruby, [14] a double asterisk is used, so x 2 is written as x ** 2. The plus–minus sign , ±, is used as a shorthand notation for two expressions written as one, representing one expression with a plus sign, the other with a minus sign.
Analogously, the inverses of tetration are often called the super-root, and the super-logarithm (In fact, all hyperoperations greater than or equal to 3 have analogous inverses); e.g., in the function =, the two inverses are the cube super-root of y and the super-logarithm base y of x.
Exponentiation for a natural power is defined as iterated multiplication, which Knuth denoted by a single up-arrow: a ↑ b = H 3 ( a , b ) = a b = a × a × ⋯ × a ⏟ b copies of a {\displaystyle {\begin{matrix}a\uparrow b=H_{3}(a,b)=a^{b}=&\underbrace {a\times a\times \dots \times a} \\&b{\mbox{ copies of }}a\end{matrix}}}
For instance, 299 792 458 m/s (the speed of light in vacuum, in metres per second) can be written as 2.997 924 58 × 10 8 m/s and then approximated as 2.998 × 10 8 m/s. SI prefixes based on powers of 10 are also used to describe small or large quantities. For example, the prefix kilo means 10 3 = 1000, so a kilometre is 1000 m.
This is a pure coincidence, as the metre was originally defined as 1 / 10 000 000 of the distance between the Earth's pole and equator along the surface at sea level, and the Earth's circumference just happens to be about 2/15 of a light-second. [39] It is also roughly equal to one foot per nanosecond (the actual number is 0.9836 ft/ns).
The four 4th roots of −1, none of which are real The three 3rd roots of −1, one of which is a negative real. An n th root of a number x, where n is a positive integer, is any of the n real or complex numbers r whose nth power is x:
Re – real part of a complex number. [2] (Also written.) resp – respectively. RHS – right-hand side of an equation. rk – rank. (Also written as rank.) RMS, rms – root mean square. rng – non-unital ring. rot – rotor of a vector field. (Also written as curl.) rowsp – row space of a matrix. RTP – required to prove.
Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 3 2, which is the number 9. In some cases when superscripts are not available, as for instance in programming languages or plain text files, the notations x ^2 ( caret ) or x **2 may be used in place of x 2 .