Newton’s notation (Section 15.3.1: Instantaneous Rate of Change) uses a dot above a variable to represent its derivative with respect to time.

Newton’s notation (Section 15.3.1: Instantaneous Rate of Change) for the second derivative (Section 15.3.5: Higher Derivatives) with respect to time.

The symbol for division (see Chapter 4: Multiplying and Dividing) is called an ‘obelus’.

This symbol means ‘therefore’. It is commonly used in proofs (Chapter 9: Proof).

This upside-down version of the ‘therefore’ symbol means ‘because’. It is sometimes used in proofs (Chapter 9: Proof).

In mathematics, the colon symbol usually means ‘such that’. It is commonly used in set-builder notation (Section 8.1.4: Set-Builder Notation).

In computer programming, this symbol is used to assign a value to a computer variable. For example, `x := 2`

might mean ‘store the number `2`

in the variable `x`

’, whereas `x = 2`

might be an expression that evaluates to either true or false depending on what is stored in `x`

. Look up ‘assignment’ in a programming manual for more information.

A dot is often used to indicate some sort of multiplication (similar to the $\times$ symbol). When used with vectors, it indicates a vector dot product (Section 11.6.1: Dot Product)

The decimal point is used to separate the integer part of a number from the fractional part (see Section 2.2.3: Decimals). In some parts of the world, the role of the comma and the dot are the other way around, so people write $12.345,67$ instead of $12,345.67$.

Sometimes this dot (the ‘baseline dot’, ‘full stop’, or ‘period’) is used instead of the centered dot $\cdot$ (‘interpunct’) to indicate multiplication, because it’s easier to type.

This symbol is called an ‘ellipsis’. It means ‘and so on’. For example, $1+2+3+\cdots + 10$ means $1+2+3+4+5+6+7+8+9+10$ (Section 7.7: Sequences). It can be used to describe sets (Section 8.1: Sets), e.g. $\{1,2,3,\ldots\}$ means the set of all natural numbers. It’s also used when writing vectors or matrices of arbitrary size (Chapter 12: Linear Algebra), for example, \[\begin{bmatrix}v_1\\v_2\\\vdots\\v_n\end{bmatrix}\] represents a vector with $n$ components.

The exclamation mark usually indicates a factorial (Section 13.3: Factorials), e.g. $4!$ means $4\times 3\times 2\times 1$. Used twice or more, it indicates that every second (or third, fourth, etc.) number is skipped, e.g. $5!!$ means $5\times 3\times 1$. This is called a ‘multifactorial’. When the exclamation mark goes before the number, it indicates a ‘subfactorial’, which is the number of ‘derangements’ (Question 13.1.2).

The exclamation mark can also be a symbol of negation, e.g. $!=$ would mean ‘not equal to’.

Dots are used in geometry diagrams to indicate points (Section 10.2: Points and Lines), and to show that two angles are equal (Section 10.3: Angles).