Infinity has intrigued humans for millennia. Aristotle categorized infinity into potential and actual forms, with potential involving abstract processes, whereas he deemed actual infinity impossible. Hesitation around infinity persisted in mathematics until Georg Cantor's advent of set theory in the late 19th century, facilitating a proper framework for dealing with infinities. Consequently, concepts like irrational numbers and infinitely large sets became foundational in mathematics. Yet, finitists contest using infinity, advocating for approaches limited to finitely constructible entities, and exploring their implications in physics.
Aristotle distinguished between two types of infinity: potential and actual. Potential infinity involves abstract scenarios with repeated processes, while actual infinity could not exist.
With set theory, Georg Cantor developed a mathematical framework to deal with infinities, which became an essential part of mathematics.
Infinities have become integral to mathematics, with innovations allowing for exploration of infinitely large sets and numbers with infinite decimal places, like pi.
Finitists reject the notion of infinity, proposing a mathematical approach based solely on finitely constructible quantities, which some aim to apply in physics.
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