I introduced friends to the idea of infinite sets of different sizes/cardinalities. They get it, but think it's silly. Where is this concept used in every day life (or in technology that is used in everyday life)?
2026-03-25 12:53:38.1774443218
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How are infinite sets of different cardinalities used practically in everyday life?
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The number of functions from natural numbers to natural numbers has a greater cardinality than the number of computable functions. This implies that there are functions that cannot be computed, no matter how powerful a computer is.
For a layperson, I would think this is a pretty interesting result that they should be able to understand. Roughly put, there are more problems than you can solve.
Admittedly, is more of a negative result than a positive one, though I suppose it makes a 'too hard to solve' verdict a little more palatable.
You won't find examples of infinite sets in everyday life. There are only finitely many atoms in the universe for example. However the distinction between countably infinite and uncountable sets is very important in modern mathematics. For example it is essential in the theory of probability, which is used very heavily in all sorts of things.