Terry J. Reedy added the comment: in-finite literally means un-limited or un-bounded. However, 'infinte' has also taken on the meaning of 'actual infinity'. So in my algorithms book, when 'actual infinities' are not in play. I describe the set of counts as unbounded. I suggest you go with just 'unlimited'. I believe constructions such as and/or (which some style guides discourage. because they are a bit ugly) should suggest some contrast or difference, rather than exact synonyms but I could be wrong.
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