4.4.2 - ToC (Maths for Regexs) Flashcards
What is a regular expression
A special sequence of characters that can be used to find or match patterns in text
What is meant by a set
an unordered collection of values in
which each value occurs at most once.
Describe this set:
A = {x |x ∈ ℕ ∧ x ≥ 1 }
he set consisting of those objects x
such that x ∈ ℕ and x ≥ 1 is true.
How do you represents empty sets
{} or Ø
What does this symbol represent: |
Such that
What does this symbol mean: ∧
AND
What does this symbol mean: ∈
“is a member of”
Give an example of compact represntation of a set
{0^n1^n| n ≥ 1} = {01, 0011, 000111, 00001111,
… }
What is a set comprehension
Set comprehension is selecting the specific values we want from a more general set.
What is meant by a countable set and what are the 2 different types
A set that can be counted off against a subset of natural numbers
What is meant by a finite set
one whose elements can be counted off by natural numbers up to a particular
number
What is meant by the cardinality of a set
the number of elements within the set
What is meant by a countably infinite set
a set that can be
counted off by the natural numbers.
What is meant by the cartesian product of 2 sets
The set of all ordered pairs (a,b) where a is a member of set A and b is a member of set B
What is meant by a proper subset
Where all the elements of the contained set is contained within another set, and there is at least one element in the containing/larger set which is not contained in the subset.
Explain what this shows:
{0, 1 , 2 } ⊂ ℕ
⊂ means proper subset of
It also shows that ℕ contains everything in {0, 1, 2 } but
there is at least one element in ℕ that is not in
{0, 1, 2 }.
What is meant by a subset
where all the elements of one set is contained within another set
What i sthe distinguishing feature between proper and normal subset
For normal subsets both sets can be equal
What is meant by a countable set
a set with the same cardinality as some subset of natural numbers.
What does A U B mean
Union where you take all the numbers from both sets a maximum of once
What does A n B mean
Intersection where you take all the members that both set have in common
What does A - B or A\B mean
Differene where you take all of the elements in a that aren’t in B
What is the set notation for A-B
A\B = {x : x ∈ A and x ∉ B}
