Set Theory in the 19th Century
Its Genesis
•
Terminology
◦
Bolzano gave us the word “set” in his 1851 publication of
Paradoxes of the Infinite
.
•
Notation
◦
Peano introduced the symbols
∩
for intersection and
∪
for union in 1888.
◦
Peano introduced the symbol
ε
for membership in 1889. Bertrand Russell gave us the
stylized
∈
in 1903.
◦
The symbol
∅
for the empty set was introduced by André Weil in 1939.
◦
Cantor introduced the enclosure of the elements of a set in curly braces
{}
in 1895.
◦
The history of the symbol
⊆
for “is a subset of” is unclear.
•
Theory
◦
Cantor is generally credited as the inventor of set theory.
Particular innovations in
cluded:
⋆
His work with infinite sets.
⋆
His break from the “PartWhole” theory of collections that was used by his pre
decessors and that had no distinction between a singleton
{
s
}
and
s
itself.
The
fundamental relationship for Cantorian set theory was that of membership.
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 Fall '10
 wen
 Set Theory, infinite sets, Actual infinity, ◦ Cantor, potential inﬁnity

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