Set theory: Difference between revisions
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Set theory is a branch of mathematics involving the study of [[Set|sets]]. These are collections of objects. Set theory is often used as a foundation for mathematics, as many mathematical objects (such as [[natural numbers]], groups, topological spaces, ...) can all be encoded as sets. In pure set theory, the primary objects of study are [[infinite]] sets, which include infinite [[Ordinal|ordinals]] and [[Cardinal|cardinals]]. Set theory is the basis for a lot of apeirology, as it provides a basis for formalising or defining apeirological concepts, and has introduced useful techniques for proof such as Mostowski collapse, or Skolem hull. Set theory is very broad, and is comprised of many other subjects such as [[proof theory]] and [[model theory]] |
Set theory is a branch of mathematics involving the study of [[Set|sets]]. These are collections of objects. Set theory is often used as a foundation for mathematics, as many mathematical objects (such as [[natural numbers]], groups, topological spaces, ...) can all be encoded as sets. In pure set theory, the primary objects of study are [[infinite]] sets, which include infinite [[Ordinal|ordinals]] and [[Cardinal|cardinals]]. Set theory is the basis for a lot of apeirology, as it provides a basis for formalising or defining apeirological concepts, and has introduced useful techniques for proof such as Mostowski collapse, or Skolem hull. Set theory is very broad, and is comprised of many other subjects such as [[proof theory]] and [[model theory]]. |
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Latest revision as of 16:17, 26 December 2023
Set theory is a branch of mathematics involving the study of sets. These are collections of objects. Set theory is often used as a foundation for mathematics, as many mathematical objects (such as natural numbers, groups, topological spaces, ...) can all be encoded as sets. In pure set theory, the primary objects of study are infinite sets, which include infinite ordinals and cardinals. Set theory is the basis for a lot of apeirology, as it provides a basis for formalising or defining apeirological concepts, and has introduced useful techniques for proof such as Mostowski collapse, or Skolem hull. Set theory is very broad, and is comprised of many other subjects such as proof theory and model theory.