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Math Help - Lexicographic Ordering

  1. #1
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    Lexicographic Ordering

    What is this? It seems alittle confusing compared to other forms of ordering.

    If we have Lex. ordering on r on A X B determined by linear order r1 on A and r2 on B. Then it would be true that if both r1 and r2 are well founded then so is r. Correct?
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  2. #2
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    Do you understand how a dictionary is ordered?
    The word “abet” comes before “about” why.
    That is Lexicographic Ordering.

    If we have lexicographic ordering on \mathbb{N} \times \mathbb{N} \times \mathbb{N} here are some examples.
    \begin{gathered}<br />
  \left( {1,3,2} \right) \prec \left( {2,1,1} \right)\text{ because } 1 < 2. \hfill \\<br />
  \left( {2,1,2} \right) \prec \left( {2,2,1} \right) \text{ because }2 = 2 \wedge 1 < 2. \hfill \\<br />
  \left( {3,3,2} \right) \prec \left( {3,3,3} \right) \text{ because }3 = 3 \wedge 3 = 3 \wedge 2 < 3. \hfill \\ \end{gathered}

    I hope this give some guidance that helps you.
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  3. #3
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    Cheers! Your amazing.
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