What are the formal names of operands and results for basic operations?
I'm trying to mentally summarize the names of the operands for basic operations. I've got this so far:
- Addition: Augend + Addend = Sum.
- Subtraction: Minuend - Subtrahend = Difference.
- Multiplication: Multiplicand × Multiplier = Product. Generally, operands are called factors.
- Division: Dividend ÷ Divisor = Quotient.
- Modulation: Dividend % Divisor = Remainder.
- Exponentiation: Base ^ Exponent = ___.
- Finding roots: Degree √ Radicand = Root.
My questions:
- I've heard addend used generally for addition operands. Is that correct formal usage?
- Do subtraction and division lack general names for their operands because they are not commutative? Or am I just ignorant of them?
- Is the base the same as a mantissa?
- Is there a formal name for the result of exponentiation?
- Is there a formal name for the operation of finding the nth root?
- Am I missing anything else?
2 Answers
$\begingroup$Found this table on Wikipedia. It has all the formal names for those operations plus logarithm.
Addition
${\left.{\begin{matrix}{\text{summand}}+{\text{summand}}\\{\text{addend (broad sense)}}+{\text{addend (broad sense)}}\\{\text{augend}}+{\text{addend (strict sense)}}\end{matrix}}\right\}}=sum$
Subtraction
${\text{minuend}}-{\text{subtrahend}}=difference$
Multiplication
$\left.{\begin{matrix}{\text{factor}}\times {\text{factor}}\\{\text{multiplier}}\times {\text{multiplicand}}\end{matrix}}\right\}=product$
Division
${\left.{\begin{matrix}{\frac {{\text{dividend}}}{{\text{divisor}}}}\\{\text{ }}\\{\frac {{\text{numerator}}}{{\text{denominator}}}}\end{matrix}}\right\}}={{\begin{matrix}fraction\\quotient\\ratio\end{matrix}}}$
Modulo
${\text{dividend}}{\bmod {\text{divisor}}}=remainder$
Exponentiation
${\text{base}}^{\text{exponent}}=power$
nth root
${\sqrt[{\text{degree}}]{{\text{radicand}}}}=root$
Logarithm
$\log _{\text{base}}({\text{antilogarithm}})=logarithm$
$\endgroup$ 3 $\begingroup$You will often see the terms in a general sum referred to as "addends" or "summands".
Your suggestion regarding subtraction/division as compared to addition/mulipilication is as good as any. The roles of the operands are not interchangeable, so a single description isn't really appropriate.
I've usually seen mantissa referring to the multiplier of a power in certain expressions. Specifically, in scientific notation. For example, in the expression $2.345\times10^8$, the mantissa would be $2.345$. It has other usage in connection with logarithms, but you can look that up.
One sometimes refers to "powers". For example, a polynomial in one variable $x$ can be described as a sum of constant multiples of nonnegative powers of $x$. Technically, the "power" is the exponent, but it is also used on occasion to refer to the entire expression (base and exponent).
Nothing comes immediately to mind regarding extracting roots.
I will comment that many of these names contain a wealth of Latin. If you happen to know Latin, you will understand their meaning more deeply. For example, "minuend" comes from a form meaning "about to be lessened" and "subtrahend" come from a form meaning "about to be taken away". In general, "-nd" will carry the meaning "about to be ---ed".
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