Definition of a sample: can it include the same object twice? Wikipedia defines a sample as:

a subset of a population.

While exploring the reason why we divide by $(n-1)$ instead of $n$ when calculating standard deviation (discussed in this question), I came across this PDF demonstrating why $(n-1)$ is better.
When listing all possible samples of $n=2$ from a population of three cards numbered 0, 2, and 4, it includes the samples (0,0), (2,2), and (4,4). I am having trouble reconciling this with the definition of a sample that I thought I knew (and that is given by Wikipedia).
A sample of 2 playing cards from a population of 52 would not include the Three of Hearts twice, would it? Likewise, I'd guess a survey of a sample of voters would not include the same voter multiple times.
Other sources back the method described in the PDF. What am I misunderstanding here?
 A: Considering your thoughtful question and the comments stream I think the answer is:
The Wikipedia article is (or rather, "was") incorrect.  A correct definition would be:

A sample is a set of observations drawn from a population by a
  defined procedure.  It may be drawn without replacement, in which case
  it is a subset of the population; or with replacement, in which case
  it is a multisubset.

A: The problem is the confusion of "plain" English with specialist jargon.  All academic disciplines and other groupings of people do it, e.g. military, individual companies, govt departments, sports, etc.  Within a discipline it is perfectly reasonable to use a term with rather more specialist overtones than in everyday language, provided that one remembers that when communicating with the general public a qualifier is usually advisable, e.g. statistical significance. Even within a discipline, as you have just found and others have already pointed out, there can be cases where a qualifier is appropriate, because the mathematical abstraction of the physical nature of a sample lends itself to potential constructs that would otherwise be physically impossible.
