What precisely is scarcity? I'm aware that certain terms in economics have precise definitions that don't necessarily line up with our intuition about what they mean. I'm currently writing a paper that heavily relies on the concept of scarcity, and I'd like to make sure I am using the term properly. Currently I have this sentence written: 


  Suppose widgets are a scarce resource that are distributed among
  agents


Then I rewrite this mathematically as $\mu = \sum\limits_{i=0}^n x_i$ where $x_i$ is the number of widgets agent $i$ has. I don't see any problems with this myself, but I'd like to make sure that economists view this as orthodox. Are there any references that I could use to verify this? Is this accurate? What is the precise definition of scarcity?

Edit

A Dictionary of Economics states scarcity is: "The property of being in excess demand at a zero price. This means that in equilibrium the price of a scarce good or factor must be positive" This is the most authoritative source I've found so far, but this doesn't seem like a rigorous definition to me - it clearly isn't mathematically defined. Am I wrong about this?
Your formula $\mu = \sum\limits_{i=0}^n x_i$ just denotes the total amount of goods, so this just means that $\mu$ units were distributed among $n$ agents. Scarcity (in this context) means that no matter how you distribute these $\mu$ units, as long as everything else is unchanged (ceteris paribus) at least one agent would like to get more, i.e. $\forall (x_i)_{i = 0}^n$ where $\mu = \sum\limits_{i=0}^n x_i$ there is an agent $i$ and a positive $\epsilon$ such that
$$
x_i \prec_i x_i + \epsilon.
$$
This is context dependent, there may be other definitions as well (e.g. ones that allow for production).