Cos 203 Flashcards
Mathematics can be classified into
Continuous and discrete maths
Explain the classification of maths
a) continuous - it is based on the continuous number line and is characterized by the fact that between any two
Numbers there is almost always
an infinite set of
numbers
b) discrete - it involves distinct numbers I.e between any two points there is a countable number of points
What is a set
A set is an unordered collection of different elements
How can set be represented with example
a) rooster/ tabular method - elements of the set are listed, bounded by two braces and separated by commas.
b) set builder notation- the set is defined by specifying a property that each element of the set have in common.
The meaning of each N Z Z^+ Q R W
N- natural number all positive integers
Z - integers all whole numbers in the number line
Z^+- all positive integers (N)
Q - rational numbers can be represented as a fraction
R - real numbers all rational and irrational numbers
What us the cardinality of a set
The number of elements in a set
What kind of function exists if the cardinality of X
a) = Y
b) is less than or equal to y
c) < y
a) Bijective function
b) injective function
c) there is an injective function but no bijective function
Venn diagram was invented by who amdnin what year
John Venn 1800
What is a venn diagram
Is a schematic diagram that shows all possible lovican relations between different mathematical set
What is set union of a&b
A U B is a set of elements which are in a, b or both
A U B = {x|x £ A or x £ B}
Set intersection of A and B
A n B is a set of elements which are in a and B
A n B ={x|x £ A and x £ B}
Set difference or relative complement of A and B
A - B is a set of elements which are in only in a but not b
A - B = {x|x £ A and x is not an element of B}
Cartesian product or cross product of set a and b
What is the power set of set x
Its the set of all subset of x including its empty set.
The cardinality of a power set is
2^n
