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#1 2007-07-11 12:55:54

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

The Evolution of Numbers

I have just drafted a little essay called The Evolution of Numbers

Criticisms welcome smile


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#2 2007-07-11 13:52:51

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: The Evolution of Numbers

With rational numbers, ya gotta include that q can't be 0.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2007-07-11 21:59:16

Patrick
Real Member
Registered: 2006-02-24
Posts: 1,005

Re: The Evolution of Numbers

I think he might have corrected this after you posted Ricky, but it's hard to tell since he hasn't responded, bbut it says: "Rational Numbers: {p/q : p and q are integers, q is not zero}"


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#4 2007-07-11 22:52:40

MathsIsFun
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Registered: 2005-01-21
Posts: 7,535

Re: The Evolution of Numbers

Ooh .. thanks guys.

No other issues?

A good read or drivel?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#5 2007-07-12 03:31:03

Patrick
Real Member
Registered: 2006-02-24
Posts: 1,005

Re: The Evolution of Numbers

Right after the title "Summary", it says "thaey" instead of "they". Other than that, I noticed nothing. Good read for people who havn't heard about the different number sets.


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#6 2007-07-12 15:00:23

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,562

Re: The Evolution of Numbers

It's nice to get a light history.
Excellent introduction to numbers.
Also, I wonder who was so smart to figure out to use zeros infinitely before and after a number.
See I kind of would have chosen one's, myself, and the whole adding thing would not have worked as nicely.
Like 00007 would be 11117 in my number system, but adding 11 and 11 would be 12 because 01 plus 01 is 02.
Anyway, I like your short history of numbers!!!


igloo myrtilles fourmis

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#7 2007-07-12 15:31:33

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: The Evolution of Numbers

Definitely a good read.  The only thing is that when I read through it, I got the impression that you were explaining how these numbers came to be in a historical sense.  Is that correct?  If so, I'd just double check to make sure you got the history right.  I myself know next to nothing about the history of math.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#8 2007-07-12 16:29:41

pi man
Member
Registered: 2006-07-06
Posts: 251

Re: The Evolution of Numbers

Looks good.   Very easy read.  Young students should be able to handle it as well as their parents who may need a refresher when it comes time to help out with the school work. 

In your example of the square root of -9, shouldn't you include -3i as a solution?

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#9 2007-07-12 16:39:38

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: The Evolution of Numbers

Thanks!

Yes, it is a little historical, but the history is complex, with Indians, Chinese, Arabs etc all following different paths of discovery, so I can only approximate it.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#10 2007-07-12 16:39:50

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: The Evolution of Numbers

In your example of the square root of -9, shouldn't you include -3i as a solution?

The solution to:

Is in fact:

However, when one writes square root, it just means the positive root.  This is why one must specify:

Edited to add:

Yes, it is a little historical, but the history is complex, with Indians, Chinese, Arabs etc all following different paths of discovery, so I can only approximate it.

You may wish to add a foot note or warning in the beginning to that effect.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#11 2007-07-12 18:44:58

MathsIsFun
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Registered: 2005-01-21
Posts: 7,535

Re: The Evolution of Numbers

So, Ricky, you agree it is OK to keep √(-9) = 3i ?

And I completely redid the "End Notes", how does it read now?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#12 2007-07-13 02:33:25

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: The Evolution of Numbers

Yep, looks good.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#13 2007-07-13 12:27:12

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: The Evolution of Numbers

Thanks, I might publish it on the "New Pages" page now.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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