Discrete Math - 2.1.1 Introduction to Sets

Is zero considered in the range of Z^+(positive integers) and the range of Z^-(negative integers)?

Maybe I missed something, but aren't the Real numbers the set of all rational and irrational numbers? Irrationals are not mentioned here, but are an uncountable subset of the Reals.

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In our discrete math class, natural numbers actually include 0. I have no idea why!

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"real numbers contains all numbers above" but contains irrational too, right?

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A better definition of "set" is probably : collection of unordered, unique AND well defined objects.
Any collection with repeated elements can be reduced to a set without any repeat (unique elements only).

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The real numbers are more than just "everything above" in the list.

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