Operations:
Hyper ops:
ā ā ā Ā± Ć Ć· Ā· ā ā ā
increment: S(a), a+1, a+(1)
decrement, P(a), a-1, a+(-1)
subtraction, a-b, (a)+(b)
S(a), a+1, a+(1)
add/sub = (Ā±a) + (Ā±b) = (Ā±b) + (Ā±a)
mul/div = (Ā±a) Ć (Ā±b) =
Operations and their inverses
multiplication vs division
exponentiation vs roots, logarithms
tetration (hyper-4) vs super-roots and super-logarithms
quintation/pentation, hexation, etc.
In mathematics, the super-logarithm is one of the two inverse functions of tetration. Just as exponentiation has two inverse functions, roots and logarithms, tetration has two inverses, super-roots and super-logarithms.
Arithmetic operations
Addition
summand + summand addendĀ (broadĀ sense) + addendĀ (broadĀ sense)Ā augend + addendĀ (strictĀ sense) } = sum {
\scriptstyle
\left.{
\begin{matrix}
\text{summand} + \text{summand} \\
\scriptstyle {
\text{addend (broad sense)}
} + \text{addend (broad sense)
} \\
\scriptstyle {\text{augend}}\,+\,{\text{addend (strict sense)}}
\end{matrix}
}
\right
\} = } \text{sum} summand + summand addendĀ (broadĀ sense) + addendĀ (broadĀ sense)Ā augend + addendĀ (strictĀ sense) ā } = sum Subtraction
minuend ā subtrahend = difference \text{minuend} - \text{subtrahend} = \text{difference} minuend ā subtrahend = difference Multiplication (Ć)
factor Ć factor multiplier Ć multiplicand } = product {\scriptstyle
\left.{
\begin{matrix}
\scriptstyle {\text{factor}}\,\times \,{\text{factor}}\\\scriptstyle {\text{multiplier}}\,\times \,{\text{multiplicand}}
\end{matrix}
}
\right
\} = } \scriptstyle {\text{product}} factor Ć factor multiplier Ć multiplicand ā } = product Division (Ć·)
dividend divisor Ā numerator denominator } = dividend divisor Ā numerator denominator } = fraction quotient ratio fraction quotient ratio {\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\frac {\scriptstyle {\text{dividend}}}{\scriptstyle {\text{divisor}}}}\\\scriptstyle {\text{ }}\\\scriptstyle {\frac {\scriptstyle {\text{numerator}}}{\scriptstyle {\text{denominator}}}}\end{matrix}}\right\}\,=\,} {\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\frac {\scriptstyle {\text{dividend}}}{\scriptstyle {\text{divisor}}}}\\\scriptstyle {\text{ }}\\\scriptstyle {\frac {\scriptstyle {\text{numerator}}}{\scriptstyle {\text{denominator}}}}\end{matrix}}\right\}\,=\,} {\displaystyle {\begin{matrix}\scriptstyle {\text{fraction}}\\\scriptstyle {\text{quotient}}\\\scriptstyle {\text{ratio}}\end{matrix}}} {\displaystyle {\begin{matrix}\scriptstyle {\text{fraction}}\\\scriptstyle {\text{quotient}}\\\scriptstyle {\text{ratio}}\end{matrix}}} divisor dividend ā Ā denominator numerator ā ā } = divisor dividend ā Ā denominator numerator ā ā } = fraction quotient ratio ā fraction quotient ratio ā Exponentiation
base exp = power \text{base}^{\text{exp}} = \text{power} base exp = power n-th root
r d = n \displaystyle{ \sqrt[d]{r} = n } d r ā = n
Logarithm l o g log l o g
log ā” b a s e ( a n t i l o g a r i t h m ) = logarithm \displaystyle{ \log_{base}({antilogarithm}) = \text{logarithm} } log ba se ā ( an t i l o g a r i t hm ) = logarithm