MATHEMATICS LANGUAGE AND SYMBOLS

Lesson 2

Mathematics is written in a ——- ——- that is designed to express ——- ——-.

Symbolic language and mathematical thoughts.

Language is defined as?

A systematic means of communicating ideas or feelings by the use of conventionalized signs, sounds, gestures, or marks having understood meanings.

The sign + for addition and the – sign for subtraction first appeared when?

1489 in a German arithmetic handbook.

This may have been borrowed from signs used by who?

Merchants and they used it to sign certain packages

A + & A – are marked on packages with?

A + for too much of whatever the package

contained, while A – meant too little.

Who invented the equals sign (=) and also introduced the pre-existing plus (+) and minus (−) signs to English speakers in 15557?

Robert Recorde (c. 1510-1558) was a welsh physician and mathematician.

Who introduced the "×" symbol for multiplication and the abbreviations "sin" and "cos" for the sine and cosine functions?

William Oughtred (1574 –1660) - an English mathematician and Anglican clergyman.

Who is credited with the first use of the division sign, ÷ (a repurposed obelus variant) and the symbols were used in Teutsche Algebra, published in 1659.

Johann Heinrich Rahn (1622-1676) - a Swiss mathematician

A number, a single variable or a combination of numbers, letters and operation symbols.

Algebraic Expression

In algebra what are used to represent numbers?

Variables, or letters

Any letter or symbol that represents a certain value.

Variable

A number on its own is called?

Constant

A number used to multiply a variable.

Coefficient

What are three (3) characteristics of the language of mathematics?

Precise

Concise

Powerful

Being able to make very fine distinctions.

Precise

Being able to say things briefly.

Concise

Being able to express complex thoughts with relative ease.

Powerful

What is a mnemonic used to remember the order of operations in Math problems?

GEMDAS

It is a device, such as a formula or rhyme, used as an aid in remembering.

MNEMONIC

What do you call a collections of well-defined distinct objects, ideas, or numbers.

Sets

The groups are called sets for as long as?

the objects in the group share a characteristic and are well defined.

What do you call objects contained in a set.

Elements

The pair of curly braces { } represents?

A set

A set is always represented by?

Capital letters

Can elements of a set be repeated?

No

The Greek letter Epsilon ‘∈’ will be read as?

‘an element of’, ‘belongs to’

How will you read this, x ∈ A ?

“x is an element of the set A”.

The symbol ‘∉’ stands for?

“is not an element of”.

Therefore, x ∉ A will be read as?

“x is not an element of the set A”.

What are the three methods commonly used in representation of sets?

Descriptive form

Rule or Set builder form

Roster or Tabular form

A verbal description of its elements.

Descriptive form

Describing a set by indicating the properties that its members must satisfy.

Rule or Set builder form

Listing the elements of a set inside a pair of braces { }.

Roster or Tabular form

a set of elements or members that has a limited, countable number of items where the counting process can eventually finish

Finite Set

A set with no elements.

Null Set or Empty Set

∅ , { } these symbols are for what kind of set?

Null Set or Empty Set

For what set is this symbol (⊆) for?

Subset

B is a subset of A if and only if every element of B is in A.

Subset

If B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B.

Proper subset

A diagram that shows all possible logical relations between a finite collection of different sets.

Venn diagram

We use “or” for?

Union of sets

We use “and” for?

Intersection of sets

It involves the association of an individual or object with another individual or object.

Relation

A —— is any set of one or more ordered pairs.

Relation

Is the set of first coordinates or the abscissas.

Domain

Is a the set of second coordinates or the ordinates.

Range

Relations can be displayed in different ways. True or False?

True

Is a relation in which each element of the domain corresponds to exactly one element of the range. In simple term, no two ordered pairs have the same abscissa.

Function

Each ordered pair is plotted as a point and can be used to show the relationships between values.

Graph

It’s shows the domain and range as separate clusters of values.

Mapping

It’s a graph represents a function if and only if no vertical line intersects the graph in more than one point.

Vertical Line Test