3. Mathematical Language and Translations

Mathematical Language and Symbols

A system that facilitates communication and clarifies meaning, and allows people to express themselves and maintain their identity.

Precise, Concise, Powerful.

What are the three CHARACTERISTICS OF THE LANGUAGE OF MATHEMATICS?

Precise

A characteristic of the language of mathematics meaning it is able to make very fine distinctions.

Concise

A characteristic of the language of mathematics meaning it is able to say things briefly.

Powerful

A characteristic of the language of mathematics meaning it is able to express complex thoughts with relative ease.

English Nouns

Words used to name things (like people, places, and things).

English Verbs

A part of an English sentence used to state action or being; a typical English sentence has at least one.

English Sentences

Used to state a complete thought.

Expressions

The mathematical analogue of a noun; a name given to a mathematical object of interest.

Mathematical Sentence

The mathematical analogue of an English sentence; it must state a complete thought.

Start of the Alphabet

The letters a, b, c, … are usually assumed to mean constants (fixed values).

I to N

The letters i, j, k, l, m, n are usually assumed to mean positive integers (for counting).

End of the Alphabet

The letters … x, y, z are usually assumed to mean variables (unknowns).

Mathematical Nouns

Could be fixed things, such as numbers (e.g., 15) or expressions with numbers (e.g.,

Mathematical Verbs

Could be the equals sign (=), or an inequality sign like < or >.

Mathematical Pronouns

Could be variables like x or y.

Real Numbers

Quantities, counts, and measures we can see in real life, such as counting fingers, understanding opposites, or measuring distance.

Real Number Line

A visual representation where all real numbers can be arranged in order, with positive values on the right of 0 and negative values on the left.

Counting/Natural Numbers

The first type of numbers learned by counting (e.g., 1, 2, 3, 4, 5, …).

Whole Numbers

The set of counting numbers with the addition of the concept of nothing represented by the number 0 (zero).

Integers

The set of whole numbers, including negative counting numbers, which represent opposites or removal of something.

Rational Numbers

Real numbers that can be written as a ratio of two integers (fractions); in decimal form, they are terminating or nonterminating but repeating decimals.

Irrational Numbers

Decimals which cannot be written as fractions; in decimal form, they are Nonterminating and non-repeating decimals