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◦
Along with other mathematicians of the late 1800s he was interested in the question of
representing functions with trigonometric series of the form
f(x)
=
a
0
+
∞
s
n
=
1
[a
n
cos
nx
+
b
n
sin
nx].
◦
In particular, he was interested in the question: Of what sets
S
is it true that if
f(x)
=
0
on
S
, then 0
=
a
0
=
b
1
=
a
1
=
b
2
=
a
2
= ···
?
◦
He knew it was true of
S
=
R
and of
S
=
R
minus a Fnite number of points.
◦
He knew of an operation
H
that turned one set into another and that was such that if it
was true of
S
, then it was true of
H(S)
.
◦
Applying this operation repeatedly gives more and more sets, which Cantor needed to
index somehow.
◦
His indices ended up being the ordinal numbers, including the transFnite ones.
•
Cantor
defned
a set to be inFnite if its elements could be put in a onetoone correspondence
with the elements of a proper subset of itself.
•
Two sets had the same
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This note was uploaded on 12/29/2011 for the course MATH 378 taught by Professor Wen during the Fall '10 term at SUNY Stony Brook.
 Fall '10
 wen
 Sets

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