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Not[OddQ] is not the same as EvenQ (sometimes)


Dear Mathematica experts,

Position[{2,3,4,5,6,7}, x_?(EvenQ[#]&)]
{{1}, {3}, {5}}
Position[{2,3,4,5,6,7}, x_?(!OddQ[#]&)]
{{0}, {1}, {3}, {5}}
Therefore, for this example, the pattern x_?(EvenQ[#]&) is not equivalent to
the pattern x_?(!OddQ[#]&). The latter matches with the head List of {2,3,4,5,6,7}, the former does not. But
Position[{-2,3,4,-5,6,7}, x_?(NonNegative[#]&)]
{{2}, {3}, {5}, {6}}
Position[{-2,3,4,-5,6,7}, x_?(!Negative[#]&)]
{{2}, {3}, {5}, {6}}
shows that the Head List is sometimes ignored by Position. Finally
Position[{1,3,5}, x_?(!OddQ[#]&)]
{{0}}
Position[{2,3,4,5,6,7}, x_?(!NumberQ[#]&)]
{{0}, {}}
Position[{2,3,4,5,6,7}, x_?(!Positive[#]&)]
{}
seems to show that there are really three possible outcomes  when using Not in a pattern involving the Position command. This does not occur for either the Count or Cases command where you get what you expect to get. 

Count[{1,3,5,7}, x_?(EvenQ[#]&)]
0
Count[{1,3,5,7}, x_?(!OddQ[#]&)]
0
Any explanations?

Arnold Seiken


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