Math035 (Module 1) Flashcards
Who made the Fibonacci sequence
Leonardo Bonacci
What is Leonardo Bonacci popularly known as
Fibonacci
What does fibonnaci mean?
Filius Bonnaci (Son of Bonacci)
what is leonardo bonacci also known as?
Leonardo of Pisa
Leonardo Pisano Bigollo (Leonardo the traveler from pisa)
Leonardo Fibonacci
Fibonacci wrote a
very famous book
“________________
Liber abaci
When did fibonacci write Liber abaci
1202
What does the liber abaci mean?
The book of calculation
What is fibonacci’s job
Mathematician and businessman
is an example of a recursive sequence,
obeying the simple rule that to calculate the next term one simply
sums the preceding two
Fibonacci Sequence
counting the number of
compositions of 1s or 2s that sum to a given total n:
Fibonacci Sequence Application
The Fibonacci numbers can be found
among the set of
binary strings
The number of binary strings of
length n without consecutive 1s is the
Fibonacci number
Fn+2
What is the golden ratio
1.61803
is a declarative
statement which is true or false, but not both.
proposition
is the study of how simple
propositions can come together to make more complicated
propositions.
Proposition Logic
The attribute assigned to a proposition
depending on its truthfulness or falsehood, which in
classical logic has only two possible values
Truth Value
What is the Golden ratio?
1.61803
¬ What is this?
negation
Ʌ what is this?
Conjunction
V What is this?
Disjunction
→ What is this?
Conditional
↔ What is this?
BiConditional
¬ Usage?
not
Ʌ Usage?
and/but
V usage?
or
→ Usage?
if, then, only if
↔ usage?
If and only if
is a mathematical table showing how the truth or falsity of a proposition varies with that of its components.
truth table
How does converse work?
p > q => q>p
How does inverse work?
p → q is ￢p → ￢q
How does contrapositive work?
p →q is ￢q → ￢p.
tautology?
Only true
Contradiction?
False only
Contingency?
at least 1 true and false
in logic, is a statement expressed in a way that would assume the value of true or false.
predicate or propositional function
Universal quantification of P(x) what does it use?
Ɐ
Existential quantification of P(x)
What does it use?
Ǝ
Ɐ What does it mean?
All True
Ǝ What does it mean?
> Atleast one True
If all is true = False
What does this mean? —> V = {a, e, i, o, u}
Set
V = {a, e, i, o, u} <—– What does this mean?
Element
roster or Listing Method
V = {a, e, i, o, u}
O = {1, 3, 5, 7, 9, ……}
Set-Builder Notation
A={x | x is odd and x < 10}.
B={xϵZ | 10 < x < 100} where xϵZ is read as “x is an
element of the set of integers
refers to the number of elements in a set.
Cardinality
are sets which either has no elements or has elements which could all be possibly listed down (countable).
Finite Sets
are sets whose elements cannot be listed
Infinite Sets
contains all of the elements relevant to a given discussion.
The universal set
is a set with no elements. In symbol, ∅ or { }.
Null Set
What does Union look like?
A∪B
What does Intersection Look like?
(A∩B)
What does set difference look like?
(A - B)
What does Set complement look like?
Ā)
set which contains all the elements of both the sets
Union
set containing only the elements that are common in both sets
Intersection
set whose elements are found in first set but not in second.
Set Difference (A - B)
> set whose elements are in the universal set (U) but not in the given set (A).
Set Complement (Ā)
Fibonacci’s Father
Guglielmo bonacci
What’s the triangle made up of numbers called?
Pascal’s Triangle
When to use Fn+1
When counting the number of compositions of 1s or 2s
Symbol of Negation
¬
Symbol of Conjunction
(^)
Symbol of Disjunction
V
Symbol of Conditional
→
Symbol of Bi-Conditional
↔
p > q => q>p what is this?
Converse
p → q is ￢p → ￢q what is this?
Inverse
p →q is ￢q → ￢p what is this?
Contrapositive
V = {a, e, i, o, u}
O = {1, 3, 5, 7, 9, ……}
What is this?
Roster or Listing method
A={x | x is odd and x < 10}.
B={xϵZ | 10 < x < 100} where xϵZ is read as “x is an
element of the set of integers
“What is this?”
Set-Builder Notation
A∪B “what is this?”
Union
(A∩B) what is this?
Intersection
(A - B) what is this?
Set-difference
(Ā) what is this?
Set-complement
