Humans are lazy when thinking about infinity. Usually it doesn’t matter, but sometimes, our imprecision comes with big philosophical implications. Profound logical errors permeate mathematics — in calculus and set theory in particular — due to an inaccurate conception of infinity.
The definition of “infinite” or “infinity” has slightly different meanings depending on the context, but the core concept is the same: without inherent limit. Contrary to the colloquial use of the term, infinity is not a really big number. It’s not even a really, really big number. It’s a concept that means “never ending”. Never fully encapsulated. Non-completeable. Or literally, “non-finite”.
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