You both take preposterous paths to finding out what "denumerable" means, and Al goes beyond preposterosity to presume to correct me. You could just ask me!
One standard treatment is Geoffrey Hunter's METALOGIC: AN INTRODUCTION TO THE METATHEORY OF STANDARD FIRST ORDER LOGIC: "The natural numbers are the numbers 0, 1, 2, 3, etc. A set is finite iff [if and only if] it has only a finite number of members; denumerable iff there is a 1-1 correspondence between it and the set of natural numbers (so a denumerable set is an infinite set); countable iff it is either finite or denumerable; uncountable iff it is neither finite nor denumerable (so an uncountable set is an infinite set)." (pp. 17-18)
Leblanc & Wisdom's DEDUCTIVE LOGIC (3rd ed.): "Sets of the smallest infinite size are often said to be of size...'aleph subzero'.... Such sets are called (in this book and generally) denumerable sets. The set {1,2,...,n,...} of the positive integers is denumerable, as is any set that is the same size as this one. So the set {0,1,2,...,n,...} of the natural numbers, or counting numbers, is also of size [aleph subzero]. Any set that is either finite or denumerable is said to be a countable set. An uncountable set, then, being of neither a finite size nor the smallest infinite size, is larger than any denumerable set." (p. 337)
"I hope that satisfies your morbid curiosity." (W. C. Fields) The reason I've used "denumerable" rather than "infinite" is that there are infinitely many different infinite cardinalities, but only one (the smallest one) that's been appropriate in the contexts where I've used "denumerable"--assuming that any curious skeptic unfamiliar with the term could look it up in a respectable sourcebook of logico-mathematical terminology, or just ask me.