N+1, Truth or Philosophical fallacy?

Somebody told me I have an unusual "collection" of bikes. 

 I was insulted.   We all know the  inviolate truth.  The proper number of bikes one must have is expressed by the simple mathematical formula, N+1. The word collection, in this context, refers to a purposeful accumulation of related objects.  The definition does not, nor has it ever, since it's first known written usage in 1460 (I'm not kidding, I think of shit like this.), ever implied a use or action.  A friend told me, "One cannot have too many bikes."  He is a Doctor,  I have to trust him.  (He is a PHD, but hell, still counts, right?)  Was he considering a collection?  N+1 can always be applied to the collection,

 especially here in the heart of American Consumerism.

I consider mine a "selection."  That is why the question has become one of metaphysics rather than simple mathematical truth.  I am wondering, can one realistically reach a point bordering on the remote possibility that all his dreams have been fulfilled?  Of course not.  One may have all the bikes needed from which to select, but never enough in his collection.  However, in a warped reality it may be possible to function without wanting an additional bike.

That is why I have a "selection" not a "collection." 

Selection is a word referring to a carefully chosen quality and characteristic as in "natural selection" or breeding.  The word isn't really that old.   It's first written usage was 1646 and of course comes from the word select which is a surprising spry youngster among words itself.  As a verb, select implies a choice of quality for some use or other.

So, there you have it, it's no wonder I was insulted.  

My bikes don't just sit around together like a bunch of postage stamps.  They have purpose.  On behalf of their usefulness I must pursue their defense.  Now that the metaphysical has been narrowed down, how do we translate this into physical and mathematical truth.  I have irrefutably (in my world) established that the application of the inviolable truth, N+1, applies to a collection of bikes. When usage is satisfied and all available selections are utilized during the resolution of the needs, how can we express it mathematically ?  Is "N" too simple an expression?  I think  -1 represents the elimination of need, N still represents the current number of bikes owned and +1 equals the continuing desire for frivolous accumulation.  

So, the rational cyclist can reach a mathematical equilibrium with a balanced equation -1N+1=N.

That is how I talk myself out of building a fixie!