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I am curious of that words; 'family' and 'set.

Some use the set of the blah-blah-blah~.

However, the other some use the family of the blah-blah-blah~.

For example, we express $X=\{v_i\}_{i=1}^N$ as

  1. $X$ is a set of $N$ vectors $v_1, v_2, \ldots, v_N$.
  2. $X$ is a family of $N$ vectors $v_1, v_2, \ldots, v_N$.

How can I understand the diffence between them?

Trevor Gunn
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Danny_Kim
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1 Answers1

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In a set, all elemens (here: vectors) are necessarily different - it doesn't recognize duplicates.

Families, however, are indexed, and thus can contain the same thing (in this case, vectors) multiple times.

Desiato
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