Concept
Can an infinite set be defined extensionally?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"You might think, by the way, that there’s no way to define an infinite set extensionally, since that would require infinite paper. This isn’t true, though, if we creatively use an ellipsis: I = { 3 , 6 , 9 , 12 , 15 , . . . } This is an extensional definition of I , since we’re explicitly listing all the members. It could be argued, though, that it’s really intensional, since the interpretation of “…” requires the reader to figure out the rule and mentally apply it to all remaining numbers. Perhaps in reality we are giving an intensional definition, cloaked in an extensional-looking list of members. I’m on the fence here."
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