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Moreover, however, while Dedekind-infinite implies your notion even without the Axiom of Choice, your definition does not imply Dedekind-infinite if we do not have the Axiom of Choice at hand your definition is what is called a "weakly Dedekind-infinite set", and it sits somewhere between Dedekind-infinite and finite that is, if a set is Dedekind ... This aspect of Infinite Scrolling When To Use It When To Avoid It plays a vital role in practical applications.
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