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No, it is impossible. Intuitively, a negative number sits at the left of 0 on the number line, and a positive number sits at the right of 0 on the number line. And a number x is greater than another number y if x sits at the right of y on the number line. So, every positive number is greater than any negative number.
Also, by definition, a positive number is greater than 0, and a negative number is smaller than zero. So, if x is positive and y is negative, you have
and since the relation of order "<" is transitive, this implies