(New page: What is cyclic? I am really confused on this defination. --~~~~) |
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--[[User:Akcooper|Akcooper]] 12:43, 16 September 2008 (UTC) | --[[User:Akcooper|Akcooper]] 12:43, 16 September 2008 (UTC) | ||
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| + | I'll try to answer both of your questions here. It's possible to create a group by taking all the powers of g (i.e. <math>g^{k} \forall k\in{\mathbb Z}</math>). If there is a <math>g^{k}=1</math> for some k > 0, then the powers of g just start over again and start "cycling". Note that when I say "powers", I'm referring to repeated application of whatever "multiplication" is defined to mean. g is called a "generator" of the group because the group can be "generated" by taking all the powers of g, and the group is "cyclic" because there is a finite value of k (this value is also equal to the order of g) where the powers of g stop producing new values and start to repeat the old ones, thus "cycling". | ||
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| + | --[[User:Dfreidin|Dfreidin]] 22:58, 16 September 2008 (UTC) | ||
Latest revision as of 17:58, 16 September 2008
What is cyclic? I am really confused on this defination.
--Akcooper 12:43, 16 September 2008 (UTC)
I'll try to answer both of your questions here. It's possible to create a group by taking all the powers of g (i.e. $ g^{k} \forall k\in{\mathbb Z} $). If there is a $ g^{k}=1 $ for some k > 0, then the powers of g just start over again and start "cycling". Note that when I say "powers", I'm referring to repeated application of whatever "multiplication" is defined to mean. g is called a "generator" of the group because the group can be "generated" by taking all the powers of g, and the group is "cyclic" because there is a finite value of k (this value is also equal to the order of g) where the powers of g stop producing new values and start to repeat the old ones, thus "cycling".
--Dfreidin 22:58, 16 September 2008 (UTC)
