# Math Terminology

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I had a minor stroke a few years back. One of the things it did to me was take away a large portion of my vocabulary. I can still think in concepts, but I can’t always remember the words for the concept. This page is where I can keep notes about mathematical terminology.

There isn’t much here to interest most people unless you are new to math and/or are looking for beginner-level information.

## Integers

The integers consist of $$0$$, the natural numbers ($$1, 2, 3, …$$), and their negatives ($$-1, -2, -3, …$$). The set of all integers is usually denoted by $$\rm{Z}$$ (or $$\rm{Z}$$ in blackboard bold, $$\mathbb{Z}$$), which stands for Zahlen (German for “numbers”).

When you add $$a$$ and $$b$$, $$a$$ and $$b$$ are both called the addends. The result is the sum.

$$a \textrm{ + } b = \textrm{addend} \textrm{ + } \textrm{addend} = \textrm{sum}$$

## Subtraction

When you subtract $$b$$ from $$a$$, $$a$$ is the minuend and $$b$$ is the subtrahend. The result is the difference.

$$a \textrm{ – } b = \textrm{minuend} \textrm{ – } \textrm{subtrahend} = \textrm{difference}$$

## Multiplication

When you multiply $$a$$ by $$b$$, $$a$$ is the multiplicand and $$b$$ is the multiplier, both numbers are called factors. The result is the product.

$$a × b = \textrm{multiplicand} × \textrm{multiplier} = \textrm{factor} × \textrm{factor} = \textrm{product}$$

### Capital Pi ($$\Pi$$) Notation

$$\prod\limits_{i=1}^{n} i$$ $$\prod_{i=1}^{4} i = 1 × 2 × 3 × 4$$ $$\prod_{i=1}^{4} i = 24$$

## Division

When you divide $$a$$ by $$b$$, $$a$$ is the dividend and $$b$$ is the divisor. The result is the quotient.

$$a \div b = \textrm{dividend} \div \textrm{divisor} = \frac{a}{b} = \frac{\textrm{dividend}}{\textrm{divisor}} = \textrm{quotient}$$

If you are doing integer division—also called “Euclidean division” or “division with remainder”—the remainder is the modulus. $$a \textrm{ modulo } n$$ (abbreviated as $$a \textrm{ mod } n$$) is the remainder after the division. For example:

 $$5 \textrm{ mod } 2 = 1$$ because $$5 \div 2 = 2$$ with a remainder of $$1$$ $$9 \textrm{ mod } 3 = 0$$ because $$9 \div 3 = 3$$ with a remainder of $$0$$