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)


Mathematics uses symbols instead of words:

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

Letter Conventions

Often (but not always) letters 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, ..., 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.


y = ax + b

People would assume that a and b are fixed values,

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

Nouns, Verbs, Sentences

Even though we don't use the words "noun", "verb", or "pronoun" in Mathematics, you 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
And they could be put together into a Sentence like this:

3x + 7 = 22

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