Arithmetic operations

Operations:

• increment

• decrement

• addition

• subtraction

• multiplication

• divisions

• integer division

• modulo

• exponentiation

• square

• cube

• roots

• logarithm

Hyper ops:

• level0 Successor

• level1 Addition

• level2 Multiplication

• level3 Exponentiation

• level4 Tetration

• Pentation

• Hexation

• etc.

∞ ≈ ≠ ± × ÷ · √ ∈ ∉

increment: S(a), a+1, a+(1)

• decrement, P(a), a-1, a+(-1)

  • addition, a+b, (a)+(b)

• subtraction, a-b, (a)+(b)

S(a), a+1, a+(1)

• inc/dec = (±a) + (±1)

• add/sub = (±a) + (±b) = (±b) + (±a)

• mul/div = (±a) × (±b) =

Operations and their inverses

1. increment vs decrement

2. addition vs subtraction

3. multiplication vs division

4. exponentiation vs roots, logarithms

5. tetration (hyper-4) vs super-roots and super-logarithms

6. 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.

\begin{align} \text{increment}: & \quad n+1 \quad & decrement n-1 \\ \text{addition}: & \quad n+x \\ \text{multiplication}: & \quad n*x \\ \text{exponentiation}: & \quad n^x \\ \text{tetration}: & \quad ^xn \end{align}

Arithmetic operations

Addition

$${ \scriptstyle \left.{ \begin{matrix} \text{summand} + \text{summand} \\ \scriptstyle { \text{addend (broad sense)} } + \text{addend (broad sense) } \\ \scriptstyle {\text{augend}}\,+\,{\text{addend (strict sense)}} \end{matrix} } \right \} = } \text{sum}$$

Subtraction

$$\text{minuend} - \text{subtrahend} = \text{difference}$$

Multiplication (×)

$${\scriptstyle \left.{ \begin{matrix} \scriptstyle {\text{factor}}\,\times \,{\text{factor}}\\\scriptstyle {\text{multiplier}}\,\times \,{\text{multiplicand}} \end{matrix} } \right \} = } \scriptstyle {\text{product}}$$

Division (÷)

$${\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\frac {\scriptstyle {\text{dividend}}}{\scriptstyle {\text{divisor}}}}\\\scriptstyle {\text{ }}\\\scriptstyle {\frac {\scriptstyle {\text{numerator}}}{\scriptstyle {\text{denominator}}}}\end{matrix}}\right\}\,=\,} {\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\frac {\scriptstyle {\text{dividend}}}{\scriptstyle {\text{divisor}}}}\\\scriptstyle {\text{ }}\\\scriptstyle {\frac {\scriptstyle {\text{numerator}}}{\scriptstyle {\text{denominator}}}}\end{matrix}}\right\}\,=\,} {\displaystyle {\begin{matrix}\scriptstyle {\text{fraction}}\\\scriptstyle {\text{quotient}}\\\scriptstyle {\text{ratio}}\end{matrix}}} {\displaystyle {\begin{matrix}\scriptstyle {\text{fraction}}\\\scriptstyle {\text{quotient}}\\\scriptstyle {\text{ratio}}\end{matrix}}}$$

Exponentiation

• base, exponent, power

$$\text{base}^{\text{exp}} = \text{power}$$

n-th root

• symbol: √

• latex: \sqrt[d]{r}

• operands:

  • degree, d

  • radicand, r

  • root, n

• common roots:

  • n: nth root

  • n=2: square root

  • n=3: cubic root

$\displaystyle{ \sqrt[d]{r} = n }$

Logarithm $log$

$\displaystyle{ \log_{base}({antilogarithm}) = \text{logarithm} }$