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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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    The first is dead wrong. May be a record for Wikipedia as the earliest ridiculous assertion in an entry.2012-10-20
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    How can the square of ANY number be equal to zero unless that number IS zero in the first place?2012-10-20
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    The Wikipedia page on [complex numbers](http://en.wikipedia.org/wiki/Complex_number) defines of a *purely imaginary number* to be "a complex number whose real part is zero" which, of course, includes $0$.2012-10-20
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    The intent is "an imaginary number is a complex number whose square is a real number $\le 0$". Not everyone considers the complex number $\:0 = 0 + 0\cdot i\:$ to be imaginary.2012-10-20
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    @BillDubuque, I would say that your comment is the answer.2012-10-20
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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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