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.
Similarities to English
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) | 42 |
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 | xy2 | -3/x |
An Adjective could be a subscript like the "n" in xn
And they could be put together into a Sentence like this:
3x + 7 = 22
(And we actually do use the word sentence in mathematics!)