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A little story
::::::Presumably the purpose of articles like this is to provide accurate information, not to confirm misconceptions caused by terminology. Plenty of people use complex numbers regularly, and just because many people don't isn't a reason to have an inaccuracy in the article.--[[User_talk:Recorder|Recorder]] 17:42, 17 August 2008 (EDT)
::::::Presumably the purpose of articles like this is to provide accurate information, not to confirm misconceptions caused by terminology. Plenty of people use complex numbers regularly, and just because many people don't isn't a reason to have an inaccuracy in the article.--[[User_talk:Recorder|Recorder]] 17:42, 17 August 2008 (EDT)
::::::In the physical world, it is not possible to find a line segment of length <math>\pi cm</math> (or even of length 1 cm), you may find approximations. For ''normal people'', this may be of no interest. So, for them, we can skip the hole ''real is more real than imaginary'' stuff. We shouldn't mislead more interested pupils by this entry: in mathematics, you go from the simple to the more complex, but not from the ''real'' to the ''surreal''. --[[User:DiEb|DiEb]] 17:52, 17 August 2008 (EDT)
::::::In the physical world, it is not possible to find a line segment of length <math>\pi cm</math> (or even of length 1 cm), you may find approximations. For ''normal people'', this may be of no interest. So, for them, we can skip the hole ''real is more real than imaginary'' stuff. We shouldn't mislead more interested pupils by this entry: in mathematics, you go from the simple to the more complex, but not from the ''real'' to the ''surreal''. --[[User:DiEb|DiEb]] 17:52, 17 August 2008 (EDT)
==The Four Number Systems==
Ok, this is something I remember getting taught in advanced maths a couple of years back.
At the beginning of modern arithmetic there was only one number system consisting of '''integers'''. You could add/subtract/multiply/divide, but you couldn't work with parts of numbers, which became a problem if you wanted to, say, divide 3 by 2.
To overcome this a second number system involving '''fractions''' and decimals was developed. Once again this worked for some time, but as maths and engineering grew people came to realise that they could not use trigonometric ratios or square roots with many numbers. They found that many of their answers could not be expressed as a fraction, and that there was seemingly no pattern to their decimal digits.
This lead to the development of a third number system, using surds to represent '''irrational numbers'''. This worked well for some time, and as all the numbers could be plotted on an ordinary axis (although a computer would be needed to plot the irrational ones) they were referred to as '''real numbers'''. However, there were still some numbers which could not be represented, those involving the square root of a negative number.
Finally, a fourth number system was developed, which incorporated '''imaginary numbers'''. Unlike the numbers found in the previous three systems these could not be represented on a normal graph, which lead to the development of the complex plane.
The moral of the story is that "real numbers" are "real" because they can be represented on a standard graph, "imaginary numbers" are "imaginary" because they cannot.
Now, looking at Wikipedia it seems this story is a rather simplistic summary of history, but then again my maths teacher was only using it to introduce us to the imaginary number system. Nonetheless it does show that imaginary numbers do actually exist, even if they may seem somewhat absurd to us. [[User:NormanS|NormanS]] 18:54, 23 August 2008 (EDT)