Are all numbers properly classified in the real number system?

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Discussion Overview

The discussion revolves around the classification of numbers within the real number system, including sets such as natural numbers, integers, rational numbers, and irrational numbers. Participants are examining the relationships and hierarchies among these sets, potentially in the context of a diagram or visual representation.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant seeks validation on their classification of various sets of numbers, specifically asking for feedback on a diagram they created.
  • Another participant corrects the initial classification by stating that natural numbers should be represented completely within the integers.
  • A third participant asserts that natural numbers, integers, and rational numbers are contained within the real numbers according to common definitions, while noting that irrational numbers can be viewed differently depending on the context.

Areas of Agreement / Disagreement

Participants express differing views on the classification of irrational numbers, indicating that there is no consensus on how they should be categorized within the real number system.

Contextual Notes

Some definitions and classifications may depend on specific mathematical contexts or interpretations, which are not fully resolved in the discussion.

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