Class
10:
Set
Cardinality
Introducing
Induction
cs2102:
Discrete
Mathematics
|
F17
uvacs2102.github.io
David
Evans
|
University
of
Virginia
Slide 2
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Plan
Set
Cardinality
Introducing
Induction
PS4
Questions
(Induction
Practice)
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Alternate
Definition
The
cardinality of
the
set
ℕ"
=
∈ ℕ ∧ <
}
is
.
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Alternate
Definition
The
cardinality of
the
set
ℕ"
=
∈ ℕ ∧ <
}
is
.
If
there
is
a
bijection between
two
sets,
they
have
the
same
cardinality.
Slide 5
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Example
What
is
the
cardinality
of
{
1, 2, 3, 4, 6
} ?
The
cardinality of
the
set
"
=
∈ ℕ ∧ <
}
is
.
If
there
is
a
bijection between
two
sets,
they
have
the
same
cardinality.
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Relations
and
Sizes
function: ≤ 1
out injective: ≤ 1 in
total: ≥ 1
out surjective: ≥ 1 in
If
there
is
a
surjective
relation
between
and
what
do
we
know
about
their
sizes?
Slide 7
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Relations
and
Sizes
function: ≤ 1
out injective: ≤ 1 in
total: ≥ 1
out surjective: ≥ 1 in
If
there
is
a
surjective
function
between
and
what
do
we
know
about
their
sizes?
Slide 8
Slide 8 text
Relations
and
Sizes
function: ≤ 1
out injective: ≤ 1 in
total: ≥ 1
out surjective: ≥ 1 in
If
there
is
a
total
surjective
injective
function
between
and
what
do
we
know
about
their
sizes?
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Union
Cardinality
What
is
the
cardinality
of
∪ ?
The
cardinality of
the
set
"
=
∈ ℕ ∧ <
}
is
.
If
there
is
a
bijection between
two
sets,
they
have
the
same
cardinality.
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Power
Set
The
power
set
of
A
is
the
set
of
all
subsets
of
A.
∈ ⟺ ⊆
Slide 11
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Power
Set
The
power
set
of
A
is
the
set
of
all
subsets
of
A.
∈ ⟺ ⊆
Is
∅ ∈ ?
Slide 12
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Power
Set
The
power
set
of
A
is
the
set
of
all
subsets
of
A.
∈ ⟺ ⊆
Is
∈ ?
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Induction
Principle
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No content
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PS4
Questions
(I
will
talk
about
problem
10.)
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Charge
• PS4
Due
Friday
(6:29pm)
• Next
week:
– “Strong”
Induction
(MCS
5)
– Induction
Practice