Counting uniques
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Much of my disreputable youth was spent in company of mathematicians. Not surprisingly, I acquired some of their habits of speech. Later I worked adjacent to the web publishing industry and there had to endure abominable abuses of language. People would speak of 'counting unique visitors', or worse still, 'counting uniques'.
Such talk arose when discussing the measurement of website traffic. During a given time interval a site might serve many visitors, with the same person sometimes visiting the site more than once. Those charged with measuring site traffic did not want to count the same visitor more than once. They wanted to know how many different visitors the site had during the interval in question. This was the problem of 'counting uniques'. Hold that thought.
The equation x+1=3 has exactly one solution: x=2. When an equation has one and only one solution, that solution is said to be unique. By way of contrast, consider the equation x*x=1. It has two solutions: x=1 is one, x=-1 is another. The equation is said to have two distinct solutions. The second equation does not have a unique solution precisely because it has two distinct solutions. The terms unique and distinct stand in contrast to one another. One does not ask about the number of unique solutions, because there can be only one. But one might well inquire about the number of distinct solutions to an equation.
My associates in the web publishing industry wanted to know the number of unique distinct visitors to a site. Counting the number of unique anything is pointless. If something is unique, then there is only one such thing. That is what unique means.