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Naïve Set Theory

The study of naïve set theory.

Sequence of Expressions

Axiom

Axiomatic theories

Axiomatic set theory was developed in response to these early attempts to understand sets, with the goal of determining precisely what operations were allowed and when.

Theorem

Cantor's Theorem

Intermediate

For any set

A

, the set of all subsets of

A

(the power set of

A

) has a strictly greater cardinality than

A

itself.\n

|P(A)| > |A|

Definition

Naïve Set Theory (Definition)

Sets are defined by a property

P(x)

, i.e.,

S = \{x \mid P(x)\}

. This allows for Russell's Paradox.