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#1 2006-10-20 16:46:37
- MathsIsFun
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Common Number Sets
Just made Common Number Sets.
I need it reviewed by set experts, including the illustration at the end.
Also Algebraic Number and Transcendental Numbers please.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#2 2006-10-20 17:01:59
- justlookingforthemoment
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Re: Common Number Sets
I'm no set expert, but it's easy to undertand and looks good. 
#3 2006-10-21 01:20:53
- Devantè
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Re: Common Number Sets
I see no mistakes in the page. However, I spotted something relatively minor and won't probably make a difference, anyway:
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.
#4 2006-10-21 02:05:05
- mathsyperson
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Re: Common Number Sets
Very good stuff! I like the "MathsIsFun Advanced" page. It's probably been up for ages and I just hadn't seen it. Or maybe I even had seen it and had just forgotten. But whatever. It's very good.
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?
Why did the vector cross the road?
It wanted to be normal.
#5 2006-10-21 08:50:45
- MathsIsFun
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Re: Common Number Sets
Great feedback, guys, thanks!
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 (i2 + 1 = 0), but I don't think ALL imaginary numbers are Algebraic, for example iπ
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#6 2006-10-23 21:38:27
- MathsIsFun
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Re: Common Number Sets
Any other feedback here?
I just feel I may be sailing close to the wind on some of my definitions.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman