|
Big_Dub
I'm just some guy



Registered: 01/12/11
Posts: 2,640
Loc: Los Angeles
Last seen: 38 minutes, 22 seconds
|
Group Theory 1
#26596696 - 04/12/20 08:56 PM (3 years, 9 months 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.
-------------------- split_by_nine said: click me you fuck do the right thing
|
board_control
Stranger
Registered: 08/09/20
Posts: 13
Last seen: 3 years, 4 months
|
Re: Group Theory [Re: Big_Dub] 1
#26874620 - 08/11/20 08:29 AM (3 years, 5 months 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
I'm just some guy



Registered: 01/12/11
Posts: 2,640
Loc: Los Angeles
Last seen: 38 minutes, 22 seconds
|
|
haha yeah category theory is a really interesting . Mathematics is so bizarre. It gets so abstract and detached from reality
-------------------- split_by_nine said: click me you fuck do the right thing
|
Big_Dub
I'm just some guy



Registered: 01/12/11
Posts: 2,640
Loc: Los Angeles
Last seen: 38 minutes, 22 seconds
|
Re: Group Theory [Re: Big_Dub] 1
#26914725 - 09/02/20 10:43 PM (3 years, 4 months ago) |
|
|
Not even sure why I posted this on here. So many great books on Abstract Algebra already!
-------------------- split_by_nine said: click me you fuck do the right thing
|
Cherk
Fashionable


Registered: 10/25/02
Posts: 46,493
Loc: International
Last seen: 1 year, 2 months
|
Re: Group Theory [Re: Big_Dub] 1
#26982653 - 10/13/20 12:05 AM (3 years, 3 months ago) |
|
|
what about (x - 1)/2 = ( y + 1)/2
what does that tell us?
--------------------
I have considered such matters. SIKE
|
Cherk
Fashionable


Registered: 10/25/02
Posts: 46,493
Loc: International
Last seen: 1 year, 2 months
|
Re: Group Theory [Re: Cherk] 1
#26982654 - 10/13/20 12:08 AM (3 years, 3 months ago) |
|
|
zorro bitches!
--------------------
I have considered such matters. SIKE
|
Big_Dub
I'm just some guy



Registered: 01/12/11
Posts: 2,640
Loc: Los Angeles
Last seen: 38 minutes, 22 seconds
|
Re: Group Theory [Re: Cherk] 1
#26986194 - 10/14/20 11:10 PM (3 years, 3 months ago) |
|
|
what do you mean by "x" and what do you mean by "y"
-------------------- split_by_nine said: click me you fuck do the right thing
|
dark_leviathan
Stranger


Registered: 12/04/19
Posts: 67
Last seen: 2 days, 21 hours
|
Re: Group Theory [Re: Cherk] 1
#26993484 - 10/19/20 07:03 PM (3 years, 3 months 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.
|
Big_Dub
I'm just some guy



Registered: 01/12/11
Posts: 2,640
Loc: Los Angeles
Last seen: 38 minutes, 22 seconds
|
|
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.
-------------------- split_by_nine said: click me you fuck do the right thing
|
ApostleofAzathoth
lunatic wielding pressure cooker



Registered: 11/16/17
Posts: 697
Loc: Somewhere in the PNW
|
Re: Group Theory [Re: Big_Dub] 1
#27445734 - 08/27/21 10:00 PM (2 years, 4 months ago) |
|
|
Can you define binary?
|
Big_Dub
I'm just some guy



Registered: 01/12/11
Posts: 2,640
Loc: Los Angeles
Last seen: 38 minutes, 22 seconds
|
|
Are you asking about the etymology of binary?
-------------------- split_by_nine said: click me you fuck do the right thing
|
ApostleofAzathoth
lunatic wielding pressure cooker



Registered: 11/16/17
Posts: 697
Loc: Somewhere in the PNW
|
Re: Group Theory [Re: Big_Dub] 1
#27445758 - 08/27/21 10:30 PM (2 years, 4 months ago) |
|
|
No, the definition. What makes a given operation binary?
|
Big_Dub
I'm just some guy



Registered: 01/12/11
Posts: 2,640
Loc: Los Angeles
Last seen: 38 minutes, 22 seconds
|
|
It takes two arguments
-------------------- split_by_nine said: click me you fuck do the right thing
|
ApostleofAzathoth
lunatic wielding pressure cooker



Registered: 11/16/17
Posts: 697
Loc: Somewhere in the PNW
|
Re: Group Theory [Re: Big_Dub] 1
#27446587 - 08/28/21 04:18 PM (2 years, 4 months ago) |
|
|
Thanks! Nice thread btw.
|
|