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
- Thre are symbols for operations: + - x /
- And symbols that "stand in" for values: x, y, ...
- And many special symbols: = < ≤, ...
Letter Conventions
Often (but not always) letters have special uses:
| |
Examples |
What they ususally 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.
Example:
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
We can think of certain symbols as being nouns and verbs, like in English
Nouns
Nouns would be fixed things, such as numbers or expressions with numbers
Pronouns
in English pronouns are things that stand in for nouns (it, he, you, etc). In math they would be variables :
Verbs
And the verb would be the equals sign "=", or maybe an inequality like < or >
Sentence
So a sentence would have nouns, pronouns, and a verb:
3x + 7 = 22
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