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Difference between revisions of "AoPS Wiki:Article of the Day"

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Today's featured article is:
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Today's featured article is '''complex number''':
  
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<blockquote class="toccolours" style="float:none; padding: 10px 15px 10px 15px; display:table; background:lime;"> The notion of a '''set''' is one of the fundamental notions in mathematics that is difficult to precisely define. Of course, we have plenty of synonyms for the word "set," like collection, ensemble, group, etc., but those names really do not define the meaning of the word set; all they can do is replace it in various sentences. So, instead of defining what sets are, one has to define what can be done with them or, in other words, what axioms the sets satisfy. These axioms are chosen to agree with our intuitive concept of a set, on one hand, and to allow various, sometimes quite sophisticated, mathematical constructions on the other hand. For the full collection... ([[set|more]])
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<font color="#B2B7F2" style="font-size:40px;">“</font>The '''complex numbers''' arise when we try to solve [[equation]]s such as <math> x^2 = -1 </math>.
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We know (from the [[trivial inequality]]) that the square of a [[real number]] cannot be [[negative]], so this equation has no solutions in the real numbers. However, it is possible to define a number, <math> i </math>, such that <math> i = \sqrt{-1} </math>. If we add this new number to the reals, we will have solutions to <math> x^2 = -1 </math>. It turns out that in the system that results... [[[complex number|more]]<font color="#B2B7F2" style="font-size:40px">”</font>
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[[User:Temperal/aotd/archive|Past AotD's found here.]]
 
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Revision as of 18:22, 25 November 2007

Temperal

Today's featured article is complex number:

“The complex numbers arise when we try to solve equations such as $x^2 = -1$.

We know (from the trivial inequality) that the square of a real number cannot be negative, so this equation has no solutions in the real numbers. However, it is possible to define a number, $i$, such that $i = \sqrt{-1}$. If we add this new number to the reals, we will have solutions to $x^2 = -1$. It turns out that in the system that results... [[[complex number|more]]”

Past AotD's found here.

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