infinito

Infinity, or infinito in several languages, is a concept describing something without bound or end. It is not a number, but an idea used to describe unbounded growth, limits, or the size of sets that are not finite. The symbol ∞, introduced by John Wallis in the 17th century, is commonly used to denote infinity. A key distinction is between potential infinity, an unbounded process that could continue indefinitely, and actual infinity, a completed infinite total.

In mathematics, infinity is central to calculus, analysis, and set theory. Infinite sets such as the natural numbers are not finite; Cantor showed that some infinities are bigger than others via cardinality, using concepts such as aleph numbers. Infinite series can converge or diverge, with limits defining their sum. The idea of limits enables calculus to formalize infinite processes. In geometry, lines and planes can extend without bound, and many theorems involve idealized infinite constructions.

Philosophically, infinity has long challenged thinkers. Zeno’s paradoxes and the notion of infinite regress question motion, knowledge, and justification, while Aristotle distinguished potential infinity from actual infinity in the process of counting or dividing.

In physics, infinities appear in equations and idealizations, for example at singularities or in certain cosmological models. They are often interpreted as signs that a current theory is incomplete or requires new methods, such as renormalization in quantum field theory.

Historically, Greek thinkers laid the groundwork; Aristotle’s distinction between potential and actual infinity influenced later developments, while Cantor’s work on transfinite numbers formalized the concept within set theory.