the infinity sign(∞) is often used casually but it is very abstract concept and ill-defined... when there are 'infinite' natural numbers and aleph-zero is cardinality of a set of natural numbers.. is ∞ bigger than aleph-zero? or smaller? or it can't be compared?
2026-04-03 16:12:05.1775232725
Which one is bigger, infinity sign(∞) or aleph number?
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1
Infinity has a context. Like everything else in mathematics. The $\infty$ sign in calculus is more order theoretic than anything else, signifying that something grows unbound. This is why it's not an issue using it for limits of functions of the reals, and limits of sequences of the natural numbers.
Cardinal numbers are something completely different. They come to give some notion of a size of a set.
Asking which one is bigger is missing the fact they don't even "share the same meaning" as far as infinities go.
You might also be interested in The Aleph numbers and infinity in calculus.