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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”).

## Addition

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 \(0\) |