by neufer » Sun May 16, 2010 3:11 am
beyond wrote:5 is not a quick simple answer! It is an odd number. Odd numbers are not simple. Even numbers are simple.
However, two odds make a simple right answer if they are equal to 2x50% of the even number equivalent. Simple - is'nt it??
<<A number n is called
simple number if the product of its proper divisors is less than or equal to n. For example: 1, 2, 3, 4,
5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 65, 67, 69, 71, 73, 74, 77, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 103, 106,....>>
The
A5 alternating group (i.e., the
even permutations of 5 objects) is the
simplest of the finite alternating
simple groups.
A5 is isomorphic to the
icosahedral rotation group (i.e.,
I of order 60):
- Simple - isn't it??
![Wink :wink:](./images/smilies/icon_wink.gif)
[quote="beyond"]5 is not a quick simple answer! It is an odd number. Odd numbers are not simple. Even numbers are simple.
However, two odds make a simple right answer if they are equal to 2x50% of the even number equivalent. Simple - is'nt it??[/quote]
<<A number n is called [color=#0000FF][b]simple[/b][/color] number if the product of its proper divisors is less than or equal to n. For example: 1, 2, 3, 4, [color=#FF0000][b]5[/b][/color], 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 65, 67, 69, 71, 73, 74, 77, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 103, 106,....>>
The [color=#FF0000][b]A[sub]5[/sub][/b][/color] alternating group (i.e., the [color=#FF0000][b]even permutations of 5 objects[/b][/color]) is the [color=#0000FF][b]simplest[/b][/color] of the finite alternating [color=#0000FF][b]simple[/b][/color] groups.
[color=#FF0000][b]A[sub]5[/sub][/b][/color] is isomorphic to the [color=#FF0000][b]icosahedral rotation group[/b][/color] (i.e., [color=#FF0000][b]I[/b][/color] of order 60):
[img]http://upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Soccer_ball.svg/220px-Soccer_ball.svg.png[/img]
[list][color=#0000FF][b]Simple[/b][/color] - isn't it?? :wink:[/list]