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busy me - Lograh — LiveJournal

Friday, 28.Feb.2003

12:14 - busy me

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<bitching type="pointless" quality="whiney">
Well, after running around all week in a manner similar to the proverbial crainially-deprived chicken, I've decided to try and start using a calendaring program (outlook, to be exact, as the college has told me we *will* be using it soon) to schedule jobs.

I may not continue this practice as it is too damn depressing.

Over the past 3 hours of talking with people and fielding calls, I now am booked (as in back-to-back shite) through next Wednesday afternoon. feh. This doesn't count the stuff I have on my to-do list from the past 2 weeks that I haven't gotten to yet. :(

addendum: That's not including lunch. I accidentally forgot to schedule that as a recurring event, so it looks like Mon and Tue I get to eat while at someone's computer. joy.

</bitching>

Comments:

[User Picture]
From:gregory_geiger
Date:13:09 28.Feb.2003 (UTC)

hey.. sorry for the nonsequitor

(Link)
is your url down?

and, can you tell me what "homomorphisim" is?

thanks.
-g
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[User Picture]
From:lograh
Date:16:16 28.Feb.2003 (UTC)

Re: hey.. sorry for the nonsequitor

(Link)
da gazebo just worked for me right now.

Homomorphism (note the spelling, not "im" at the end) from Mathematics (specifically, Algebra):
"
A mapping Φ from a group G into a group H is said to be a homomorphism if for all a,b ∈ G, Φ(ab)=Φ(a)Φ(b).
"

Or, in less technical terms, a homomorphism is a mapping that can be 'distributed' (quotes because it's not technically correcct, but you get the idea) across the group operation.

Or, even more simply (and even less technically correct, but perhaps easier to understand), a homomorphism is a function f such that any time you have two numbers, a and b, then f(a*b) = f(a)*f(b).

One example could be f(x)=x. The identity function. f(5*4) = f(20) = 20 = 5*4 = f(5)*f(4).
A non-example would be f(x)=-x. f(5*4) = f(20)= -20 != 20 = -5 * -4 = f(5) * f(4).

See the problem with the second one? f would flip the sign of both 5 and 4, and you'd get 20, not -20.

As a technical side-note, homomorphisms actually exist on objects other than groups, but the concept is the same. For example, a homomorphism on rings is the same as for groups, with the addition that not only is Φ(ab) = Φ(a)Φ(b), but Φ(a+b) = Φ(a)+Φ(b). Of course, most of these other objects that have homomorphisms are just specialized groups (like the rings above), but it's not inconcieveable that you could have a homomorphism on something unrelated to groups, and people would expect it to operate the same.
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