Are all numbers properly classified in the real number system?

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The discussion focuses on the classification of various sets of numbers within the real number system, including natural, integer, rational, and irrational numbers. A user seeks feedback on their diagram that illustrates these classifications. Corrections were suggested, specifically placing the natural numbers entirely within the integers. Participants agree that natural, integer, and rational numbers are typically considered subsets of the real numbers, while the classification of irrationals can vary. Overall, the conversation emphasizes the importance of accurate representation in mathematical diagrams.
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Have I correctly classified these sets of numbers? I am trying to diagram algebraic, transcendental, irrational...etc, numbers. Please see the attached picture.
Thanks
 

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

Surely this isn't a difficult question.
 
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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