So, how exactly does this work if one acquires and disposes of a quantity of bikes in rapid succession? If three were acquired in three weeks, and then three discharged in a week and a half, is it now simply N-3 according to the latest streak, or does it revert to N? At which point does N stabilize to the point where subsequent N+1 or N-1 takes effect?

My understanding is that N represents the largest number of bicycles owned at one time: I assume that N can increase, but can never decrease. Let t1, t2, and t3 represent three successive points in time, and let x represent an arbitrary but stable number of bicycles. Hence:

t1: x bicycles are owned. N = x; N +1 = x + 1. You have N bicycles.
t2: 3 additional bicycles are acquired. N = x + 3; N +1 = x + 4. You still have N bicycles.
t3: 3 bicycles are sold. N = x + 3, since N cannot decrease. N + 1 remains x + 4, for similar reasons. You now have N-3 bicycles.

So basically: at t1, the correct number of bicycles to own was one more than x, the number that was owned at that time. Now, the correct number of bicycles to own has increased to 4 more than you currently own.

Now, this can be avoided by discharging bicycles prior to acquiring new ones. After all, N is based upon the largest number owned at one time. Were one to discharge three bicycles, N would remain the same, and one would be at N-3. Acquiring three new ones would put one back up to N.

And, obviously, in need of one more.

You know you want a fat bike.

I need a gravel bike first. Then a fat bike.

It's COMPLICATED! but not as complex as described by @wipedoutkitty.

If the 3 added are far superior to the 3 lost, then N+(3-3) = N+

If the 3 added are about the same quality then N+(3-3) = N+

If you bought variety, but sold off quality rides then N+(3-3) = N+. You only ride one at a time, and life is too short to ride anything but a high quality machine.

ps: N = the number of bikes presently in your collection.

N represents all of the bicycles on earth.

I think what you meant was "n," which is YOUR sample.

N is the parameter.

N+3-3 = N+6
Just like boy/girlfriends, it only adds up when you count them.

Me thinks I've thunk N-uff about the above. Never was good at bike math.

N-3 = Y (why)?

It's important to remember that when adding and subtracting from N, your ability to rationalize and/or hide the economic reality of your arithmetic is vital, and sometimes N+3-3=Jimmy Choo

I'm going with this!

Domestic bliss, mostly; funds recapture, partly.

Plus, it is unfair to the bikes to just sit in my garage unused because they were replaced with better fitting, higher quality examples. One went to a lady who loved old French bikes, who had to give hers up when she moved who had a massive smile when she got back from the test ride. Another went to a guy who wanted a matching Miyata 610s with his wife for touring, so two are in a better place!

You kept the Univega road bike though, right?

Yep, sure did! The Univega was the reason the Peugeot went, I don't ride fast road bikes all that much to begin with. Having two fulfilling that role when the Univega is nicer and fits better meant the Peugeot simply was just going to bide its time til I did an Eroica or such.

Ah, Grasshopper, you have grasped well life's lessons for tranquility and happiness:
1) If you have domestic tranquility, you have chosen wisely
2) If you have made others happy (your -1 is their +1), you have chosen wisely, and
3) If you have one nice bike to ride, and you do ride it, you have chosen wisely.

dude, math

Well good decisions by you all around! cull the herd to keep what fits you best and you like the most.

I need to do this soon- 3 steel road bikes is just dumb when I dont use one of them and another is used about 10% of the time. But i like the idea of the unused bikes and thats kept me from doing anything so far.

N isn't a number– it's a quantum that changes over time and is comprised of discreet elements the value of which also change over time such that at any given time collectively the elements equate to N. Accordingly, N may actually increase over time even after certain discreet elements that previously were a part of N have been eliminated… and, vice versa.

aaaahhhhmmmmmnn.... aaaaahhhhhhhmmmmmmn..... aaaaahhhhhmmmmmmnn..

DEEP

Deep sheet, man.

You sold bikes? That's just sick.

I could argue that hoarding nice rides that are just going to collect dust when they could be loved and used by someone else is sicker

Yes, this is getting at it - as in quantum mechanics, N is a state that is only defined for sure by outside observation. The outside observer is typically a spouse. Only in the interaction between the measured and the measurer is N discovered and set.

N is always how many you have.