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The following is taken from Wikipedia's definition.

An imaginary number is a number whose square is less than or equal to zero.

But I also heard that

An imaginary number is a number whose square is less than zero.

Which is the correct one?

Edit:

My doubt came from the fact that some mathematicians consider the imaginary numbers are on the vertical axis and the real numbers are on the horizontal axis. So the intersection point at the origin. As a result, zero is included in the imaginary number set.

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    @BillDubuque: So the intersection of real number set and imaginary number set is a set that contains only one element 0? If you are sure with your comment above, you can make it as an answer and I will accept it for finalization.2012-10-21

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