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Totally ordered partition of a set

  1. Apr 8, 2012 #1
    If I have a totally ordered set and then create a noncrossing partition of that set it seems intuitively obvious that each block of the partition would be totally ordered as well. Can I assume this inheritance or do I need to prove each block is totally ordered? How would one go about proving that if it is the case.
  2. jcsd
  3. Apr 9, 2012 #2
    In general, if X is totally ordered and if [itex]A\subseteq X[/itex], then A is totally ordered.
    The proof is not difficult, just use the definition of total order.
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