# The Language of Mathematics

## The Language of Mathematics

The Language of Mathematics was designed so we can write about:

**Things** like Numbers, Sets, Functions, etc

What we **Do** with those things (add, subtract, multiply, divide, join together, etc)

## Symbols

Mathematics uses symbols instead of words:

- There are the 10 digits: 0, 1, 2, ... 9
- There are symbols for operations: +, −, ×, /, ...
- And symbols that "stand in" for values: x, y, ...
- And many special symbols: π, =, <, ≤, ...

## Letter Conventions

Letters often have special uses:

Examples | What they usually mean | |
---|---|---|

Start of the alphabet: | a, b, c, ... |
constants (fixed values) |

From i to n: | i, j, k, l, m, n |
positive integers (for counting) |

End of the alphabet: | ... x, y, z |
variables (unknowns) |

Those are **not rules**, but they are often used that way.

### Example:

y = ax + b

People will **assume** that a and b are fixed values,

And that x is the one that changes, which in turn makes y change.

## UPPERCASE vs lowercase

It is also common to use

- lowercase for variables (like x or y) or counting values (like m or n) and
- UPPERCASE for sets (like X or Y) and special constants

### Example:

A = {1, 2, 3}

Using an uppercase "A" makes it easy to tell it is a set.

It makes things clearer to read.

## Nouns, Verbs, Sentences

We don't use the words "noun", "verb", or "pronoun" in Mathematics, but we can imagine these **similarities to English**:

**Nouns**could be fixed things, such as numbers, or expressions with numbers:

15 | 2(3-1/2) | 4^{2} |

The

**Verb**could be the equals sign "=", or an inequality like < or >**Pronouns**(things like

*it*,

*he*,

*you*, etc) could be variables like

**x**or

**y**:

5x-7 |
xy^{2} |
-3/x |

An

**Adjective**could be a subscript like the "n" in x_{n} And they could be put together into a

**Sentence**like this:3x + 7 = 22

(And we actually do use the word sentence in mathematics!)