No Two Alike

One of the definitions of collecting (versus accumulating, or worse, hoarding) is the rule: No Two Alike.
     Each coin in a collection plays a specific role. Consequently, the collector strives to find the best player. Once the best is found, no duplicates are needed, as they do not add to the collection. A duplicate is just that: a coin without a role of its own -- except to trade for a coin that is needed for the collection.

This cent shows a thick green patina, probably malachite
bronchantite, exfoliating to reveal cuprite and maybe
a bit of bornite just under the chin. Gotta love it!

     We have seen that marvelous coins are singular. They have been elevated from their utility value to the outer-worldly category of collected objects. A duplicate, however, has utility: it can be traded for another coin or be held as an investment to sell later at a higher price. Hence, a duplicate is useful, not singular. No matter what you say, it is not. Duplicates are the stuff of accumulators and hoarders.
     One way to increase the breadth of a collection is to assign new roles to coins so that they do play a unique role. In this regard, we have mint marks that differentiate cents of the same date. We also have die varieties and die states. All of these categorizations make each coin unique, allowing us to follow the rule: No Two Alike.
     It is important to understand this rule in order to appreciate how coins become marvelous, and more specifically, how they become singular in the act of collecting them.
     Of course, it depends on how we define "alike." If you collect relic-coins, then the pattern of corrosion itself is the differentiating factor. Such coins, although shunned by many numismatists (undeservedly so), are unique in the way that they corrode. Even then, it depends on how the collection is organized. And so, consider the marvelous coin pictured here: an Indian cent in full bloom. It was in the ground for years. This one is steeped in history: it circulated, was lost, was probably searched for, and eventually found with a metal detector with much delight, and now you are viewing it.
     It is marvelous, and certainly singular.