I just feel I may be sailing close to the wind on some of my definitions.

]]>Devante: yes, would sound better.

Mathsy: It is a positive pain, but "Natural Numbers" does have two meanings. Number Theory: {0, 1, 2, ...}, Set Theory: {0, 1, 2, ...}.

Maybe we could compile a list ... what fields have you studied, and how did they define "Natural Numbers"?

Well "i" is Algebraic (i[sup]2[/sup] + 1 = 0), but I don't think ALL imaginary numbers are Algebraic, for example iπ

]]>I've read all the pages and they all seem mostly accurate. A few things:

I'm not entirely sure about this, but I think natural numbers start at 1 for all fields of mathematics and it's just that some fields use the non-negative integers instead. You may be right, but it just seems silly to change the definition of a natural number to fit what you're doing.

While there's nothing wrong with saying that rationals are an integer divided by an integer and that the denominator can't be 0, it's easier to say that rationals are an integer divided by a natural.

If algebraic numbers are numbers that can be solutions of a polynomial equation with rational coefficients, does that mean that imaginary numbers can be algebraic too?

]]>The whole numbers from 1 upwards

.(Or from 0 upwards in some fields of mathematics).

There shouldn't be a full stop after 'upwards', I think. If you were to remove the brackets, it would have a full stop and then another full stop on its own.

It happens somewhere else, too, I think.

I could probably be wrong.

]]>I need it reviewed by set experts, including the illustration at the end.

Also Algebraic Number and Transcendental Numbers please.

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