Some mathematical notation used in Math 375
Set notation
Examples:
{
x
:
x
∈
R
, x >
4
}
, or also
{
x
∈
R
:
x >
4
}
, denotes the set of all real numbers
which are greater than 4.
x
∈
E
means the element
x
belongs to the set
E
.
x /
∈
A
means the element
x
does not belong to
E
.
If
E
=
{
x
∈
R
:
x >
4
}
, then 5
∈
E
but 3
/
∈
E
.
For two sets
E
,
F
we write
E
⊂
F
if
E
is a subset of
F
, that is if every element
of
E
also belongs to
F
.
E
∩
F
is the intersection of
E
and
F
, that is the set which consists of those
x
which belongs to both
E
and
F
.
E
∪
F
is the union of
E
and
F
, that is the set which consists of those
x
which
belongs to either
E
or
F
or both.
∅
is the empty set which does not have any members. Observe that the empty
set is a subset of every set.
Implications:
Let
A
and
B
to statements.
“
A
=
⇒
B
” means “
A
implies
B
” (in other words this means: If A holds, then
B
holds true).
An alternative (more precise but less intuitive) form of expressing
A
=
⇒
B
is
as follows
A
=
⇒
B
is true if either
A
is false or
A
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 Fall '08
 Staff
 Calculus, Linear Algebra, Algebra, Real Numbers, Vector Space, Dot Product, Complex number, Hilbert space

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