Proper classification

ghotra

Have I correctly classified these sets of numbers? I am trying to diagram algebraic, transcendental, irrational....etc, numbers. Please see the attached picture.
Thanks

ghotra

First correction: put the natural numbers ellipse completely inside the integers. The attachment has been updated.

ghotra

...comments?

Surely this isn't a difficult question.

shmoe

naturals, integers, and rationals are contained in the reals by every definition I've seen (though there is the notion of the gaussian integers, it's field of fractions, etc). Irrationals can go either way, but the most common definition has them contained in the reals as well.

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ghotra	First correction: put the natural numbers ellipse completely inside the integers. The attachment has been updated.

shmoe Recognitions: Homework Help Science Advisor	Proper classification naturals, integers, and rationals are contained in the reals by every definition I've seen (though there is the notion of the gaussian integers, it's field of fractions, etc). Irrationals can go either way, but the most common definition has them contained in the reals as well.