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OfflineBig_Dub
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Group Theory
    #26596696 - 04/12/20 10:56 PM (7 months, 14 days ago)

Definition: Binary Operation
A binary operation on a set G is a function *: GxG -> G.
For any a,b \in G we typically write *(a,b) and a*b.

A binary operation is associative if for all a,b,c \in G we have a*(b*c) = (a*b)* c.
A binary operation is commutative if for all a,b \in G we have a*b = b*a.

Example
Addition is an associative binary operation on \Z = {0, 1, -1, 2, -2, ...}. e.g. 1+(2+3) = (1+2)+3 = 6.


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Offlineboard_control
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Re: Group Theory [Re: Big_Dub]
    #26874620 - 08/11/20 10:29 AM (3 months, 18 days ago)

It's always nice to see someone else interested in this kind of math. I've always felt like category theory is that higher level of consciousness. The area where concrete examples disappear and only arrows survive. Much like the content on the rest of this site.


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Re: Group Theory [Re: board_control]
    #26914721 - 09/03/20 12:42 AM (2 months, 26 days ago)

haha yeah category theory is a really interesting . Mathematics is so bizarre. It gets so abstract and detached from reality


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Re: Group Theory [Re: Big_Dub]
    #26914725 - 09/03/20 12:43 AM (2 months, 26 days ago)

Not even sure why I posted this on here. So many great books on Abstract Algebra already!


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OfflineCherk
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Re: Group Theory [Re: Big_Dub]
    #26982653 - 10/13/20 02:05 AM (1 month, 17 days ago)

what about (x - 1)/2 = ( y + 1)/2

what does that tell us?


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Re: Group Theory [Re: Cherk]
    #26982654 - 10/13/20 02:08 AM (1 month, 17 days ago)

zorro bitches!


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Re: Group Theory [Re: Cherk]
    #26986194 - 10/15/20 01:10 AM (1 month, 15 days ago)

what do you mean by "x" and what do you mean by "y"


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Offlinedark_leviathan
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Re: Group Theory [Re: Cherk]
    #26993484 - 10/19/20 09:03 PM (1 month, 10 days ago)

On a 2D plane, you can graph that.
(x-1)/2 = (y+1)/2

multiply both sides by 2

x-1 = y+1

subtract 1 from both sides

x-2 = y

you get a line.


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Re: Group Theory [Re: dark_leviathan]
    #26994106 - 10/20/20 10:08 AM (1 month, 10 days ago)

true. but what is x? what is y? are they sets? are they elements of a set? you cant just write x or y. you have to state where they are coming from. you cant assume that we are working with the real numbers.


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