MMW Prelim Reviewer

LANGUAGE 1

It is the system of words, signs and symbols which people use to express ideas, thoughts and feelings.

LANGUAGE 2

It consists of the words, their pronunciation and the methods of combining them to be understood by a community.

LANGUAGE 3

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

MATHEMATICAL LANGUAGE

It is the system used to communicate mathematical ideas.

NON-TEMPORAL, DEVOID OF EMOTIONAL CONTENT, PRECISE

Characteristics of Mathematical Language:

VARIABLES

any quantity which may take on different values

CONSTANT

any quantity that is fixed

MATHEMATICAL EXPRESSIONS

Consists of term/s and has no equal sign. The term is separated from other terms with either plus or minus signs

MATHEMATICAL SENTENCE

It combines two mathematical expressions (numbers and variables) using the comparison operator =, ≠, >,<)

LITERAL COEFFICIENTS

represents the unknown and makes use of letters

NUMERICAL COEFFICIENTS

the number with a variable

OPEN SENTENCE

it uses variables, meaning that it is not known whether or not the mathematical sentence is true or false.

CLOSED SENTENCE

that is known to be either true or false.

SET

It is a well-defined collection of distinct objects. It is conventionally named with capital letters.

SUBSET

It is a set every element of which can be found on a bigger set.

IMPROPER SUBSET

includes the set itself and the null set

EMPTY SET

it has no element { }

FINITE SET

has countable number of elements

INFINITE SET

has uncountable number of elements

UNIVERSAL SET

It is the totality of all the elements of the sets under consideration, and is denoted by U.

EQUAL SETS

have the exact same elements.

EQUIVALENT SETS

have the same number of elements. (number only)

JOINT SETS

have at least one common element.

DISJOINT SETS

have no common element.

Element of; set membership

A ∈ B

Union; elements that belong to set A or B

A ∪ B

Intersection; elements that belong to both set A and B

A ∩ B

Subset; has a few or all elements equal to the set

A ⊆ B

Not subset; left set is not a subset of right set

A ⊄ B