Topic 2: The Language of Mathematics

Characteristics of Mathematics Language

1. Precise – Able to make fine distinctions

2. Concise – Able to say things briefly

3. Powerful – Able to express complex thoughts with relative ease

Nouns

are used to denote people, places, things.

Sentence

are used to state complete thoughts

Expressions

mathematical analog of a “noun” are used to denote mathematical symbols, objects, characters, etc.

Mathematical sentence

are correct arrangement of mathematical symbols that express complete thoughts.

Synonyms

• refer to different name for same mathematics expressions.

• Mathematical objects have different names but they could be similar.

The equal sign “=“

one of the most popular mathematical verbs.

Four Basic Concepts

1. Sets

2. Functions

3. Relations

4. Binary operations

Set

• a well-defined collection of distinct objects.

• means that it is possible to determine whether an object belongs to

• Ex. P = {a, b, c, d}

Roster form

elements are separated by commas and enclosed by braces.

Rule form

makes use of the description {xl …}. reads “x such that”

Functions

• expression rules or laws that define relationship between one variable (the independent variable) and another variable (the dependent variable).

• behave like nouns when used in mathematical sentences.

• Ex. The square root of twenty -five is less than seven.

Relations

• relation between two sets is a collection of ordered pairs containing one object from each set.

• symbols behave like adjectives

• Refers to a property rather than an object

• Statement of relationship

Binary Operation

• Calculation that combine two elements (called operands) to produce another element.

• Acts like a conjunction that sits between two objects (nouns)

• Ex. • “two plus four”

Mathematical sentences have…

1. Verbs

2. Truth Values

3. Conventions

Different meaning of “is”

1. Denoting similarity

2. Adjectival phrase specifying a property

3. Showing an example of ...

Truth Values

Mathematical sentences can be either true or false, just as in English sentences

Conventions

Mathematics relies on specific symbols and notations (e.g., "3 + 4 = 7," "5 x 2 = 10") that must be followed.