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If I have a sequence {Pn} and I know that lim Pn = p, can I call {Pn} infinite? I am trying to use this result in a real analysis proof. I know B(p; r) intersection S is non-empty and I need to show that it has indefinitely many points. I can show that {Pn} is a subset of S and is also a subset of B(p;r). So, if {Pn} is infinite, then B(p;r) intersection S would have indefinitely many points. Our definition of {Pn} is not strictly defined. Just that n is a natural number. I know that sequences can be finite or infinite but I am not sure of the definitions. Thanks!

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# Question about sequences

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