
Big_Dub
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Group Theory
#26596696  04/12/20 10:56 PM (6 months, 11 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.


board_control
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Re: Group Theory [Re: Big_Dub]
#26874620  08/11/20 10:29 AM (2 months, 14 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.

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


Big_Dub
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Re: Group Theory [Re: Big_Dub]
#26914725  09/03/20 12:43 AM (1 month, 23 days ago) 


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


Cherk
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Re: Group Theory [Re: Big_Dub]
#26982653  10/13/20 02:05 AM (14 days, 3 hours ago) 


what about (x  1)/2 = ( y + 1)/2
what does that tell us?

I have considered such matters. SIKE

Cherk
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Re: Group Theory [Re: Cherk]
#26982654  10/13/20 02:08 AM (14 days, 3 hours ago) 


zorro bitches!

I have considered such matters. SIKE

Big_Dub
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Re: Group Theory [Re: Cherk]
#26986194  10/15/20 01:10 AM (12 days, 4 hours ago) 


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


dark_leviathan
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Re: Group Theory [Re: Cherk]
#26993484  10/19/20 09:03 PM (7 days, 8 hours ago) 


On a 2D plane, you can graph that. (x1)/2 = (y+1)/2
multiply both sides by 2
x1 = y+1
subtract 1 from both sides
x2 = y
you get a line.

Big_Dub
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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.


