Being a mathematician I take exception.

There are only 10 digits - but using only those ten digits there are infinite sets of numbers which are themselves infinite (The Reals, Rationales, Irrationals, Integers, sets (like the Cantor set), various algebras, etc.)

There are two "kinds" of infinite; one is countable like the set of all positive integers and by using proof by induction method I can show that the set of rational numbers are also countably infinite because I can essentially "map" each rational number (one-to-one - a.k.a injective) to an integer thus; the rationale set is also countable infinite (these items and methods can be found in most any first year Abstract Algebra, Topology, and some times Real Analysis (aka Advanced Calculus) text.

By reapplying the logic as it where: 10 digits (88 keys), and infinitely countable positive integers (notes one after the other infinitely - and yes there can be repeats just like 10, 100, 1000, 10000, .... think of the map of 1= c and 0 = b then cb, cbb, cbbb, cbbbb, ....).

Since music (and I am not arguing that it is good or bad music) is nothing more than a set of notes (disregarding, tempo and other attributes) I propose that the set of all music is countable infinite (akin to mapping integers to rationales)


However, I leave as home work for the reader to show
Larry

Last edited by Larry Kehl; 09/15/12 09:04 PM.
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