Lesson 2 Flashcards
__________ - is the system used to communicate mathematical ideas.
Mathematical Language
_____________ - has its own grammar, syntax, vocabulary, word order, synonyms, conventions, idioms, abbreviations, sentence structure and paragraph structure. It has certain language features unparalleled in other languages, such as representation.
Mathematical Language
______________ : Creating appropriate representations and relationships to mathematize the original problem.
Modelling and Formulating
_____________ : Changing the mathematical form in which a problem is originally expressed to equivalent forms that represent solutions.
Transforming and manipulating
___________: Applying derived results to the original problem situation, and interpreting and generalizing the results in that light.
Inferring
________________ : Reporting what has been learned about a problem to a specified audience.
Communicating
______________________ consist of terms. The terms is separated from other terms with either plus or minus signs. A single term may contain an expression in parentheses or other grouping symbols.
Mathematical Expressions
Types of Mathematical Expressions
Monomial, __________ , Trinomial
_________ 2 Terms __________
1Term, Binomial, 3 Terms
_______________ combines two mathematical expressions using a comparison operator.
Mathematical Sentence
These expressions either use numbers , variables or both. The ______________ include equal, not equal , greater than, greater than or equal to, less than, and less than or equal to.
comparison operators
A mathematical expressions containing the equal sign is an __________.
Equation
The two parts of an equation are called _________.
members
A mathematical expression containing the inequality sign is an _________.
inequality
The signs which convey equality or inequality are also called ________________ because they specify how two expressions are related
relation symbols
What is the 2 things to understand symbols?
Context, Convention
___________ (background) refers to the particular topics being studied and it is important to understand the context to understand mathematical symbols.
Context
____________ is a technique used by mathematicians, engineers, scientists in which each particular symbol has particular meaning.
Convention
A ____ is a well-defined collection of distinct objects, The objects that make up a set is called _________.
set, elements
_________ has no element and is denoted by ∅ by a pair of braces with no element inside , i.e. { }
Empty /Null /Void Set
_________ has countable number of elements , i.e. A = {1, 2, 3, 4, 5}
Finite Set
__________ has uncountable number of elements,
A = { …,-3,-2,-1,0,…}
Infinite Set
____________ is the totality of all the elements of the sets under consideration, denoted by U, i.e. U = { …-2,-1,0,1,2,…}
Universal Set
__________ have been the same elements.
Ex. A = [4, 12, 8, 9, 16]
B = [9, 8, 12, 16, 4]
Equal Sets
_______________ have the same number of elements.
Ex.
A = [A, B, C, D, E]
B = [ Jan., Feb, Mar, Apr., May]
Equivalent Sets
_________ have at least one common element.
Joint Sets
_________ have no common element.
Disjoint Sets
_______ is a set every element of which can be found on a bigger set.
Subset
other than the set itself and the null set, all are considered _________.
Proper Subset
_________ the set containing all the subsets of the given set with number of elements.
Power Set
_________________ [ denoted by AU B] is a set whose elements are found in A and B or in both . In symbol: A cup B = { x/x in A or x in B}.
Union of Sets A and B
__________________ [denoted by A n B ]is a set whose elements are common to both sets.
Intersection of Sets A and B
__________ [denoted by A - B] is a set whose elements are found in set A but not in set B. In symbol: A-B={ x/x in A and B}.
Difference of Sets A and B
________________ [ denoted by A^ prime ] is a set whose elements are found in the universal set but not in set A. In symbol: A^ prime ={ x/x EU and x notin A}
Complement of Set A
The pictorial representation of relationship and operations of set is the so called Venn -Euler Diagrams or simply ___________.
Venn Diagrams
The ___________ is usually represented by a rectangle while circles with the rectangle usually represent it _______.
Universal set, Subsets
__________ are mathematical entities that give unique outputs to particular inputs. It is consists of argument (input to a function), value (output), domain (set of all permitted inputs to given function ) and codomain (set of permissible outputs).
Functions
A _________ is a rule which associates each element of the first set with at least one element in the second set.
Relation
