Given X = {1,2,..., 100}. For x, y in X, define x # y if and only if x - y is a positive prime number. Is the # relation incomplete? I don't particularly understand the reasoning as of yet, and though I have a general idea after looking up the difference between indifferent and incomplete, I can't quite put into words why this would work for a numbered set.
Background: we are going over preferences and what makes them complete or incomplete. Here, we define the & symbol (the >= sign in the image) as the preference equation. x is preferred to y if and only if x - y is a positive prime number; I don't understand why this preference is incomplete
$x-\beta y=0$
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