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Furthermore, 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 Monkey Theorem Wikipedia plays a vital role in practical applications.
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Moreover, infinite decimals are introduced very loosely in secondary education and the subtleties are not always fully grasped until arriving at university. By the way, there is a group of very strict Mathematicians who find it very difficult to accept the manipulation of infinite quantities in any way. This aspect of Infinite Monkey Theorem Wikipedia plays a vital role in practical applications.
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Final Thoughts on Infinite Monkey Theorem Wikipedia
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