Definition:Set Theory/Historical Note

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Historical Note on Set Theory

Set theory arose from an attempt to comprehend the question: "What is a number?"

The main initial development of the subject was in fact not directly generated as a result of trying to answer this question, but as a result of Georg Cantor's work around $1870$ to understand the nature of infinite series and related subjects.

As a result of this he began to consider the nature of infinite collections of general object, not just numbers.

In $1873$, Cantor discovered that the set of algebraic reals is countable.

Soon after that, he discovered that the set of all real numbers is uncountable.

The concepts of equipotent sets, order isomorphic structures, cardinals and ordinals are all due to Cantor.

Cantor usually considered the founder of set theory as a mathematical discipline ...
-- Patrick Suppes: Axiomatic Set Theory (1960, 2nd ed. 1972)