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Shop: Kraken Kratom Red Vein Kratom   Unfolding Nature Unfolding Nature: Being in the Implicate Order

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OfflineBig_Dub
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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.


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split_by_nine said:
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Offlineboard_control
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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.


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OfflineBig_Dub
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Re: Group Theory [Re: board_control] * 1
    #26914721 - 09/02/20 10:42 PM (3 years, 4 months 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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split_by_nine said:
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OfflineBig_Dub
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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!


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split_by_nine said:
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OfflineCherk
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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?


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I have considered such matters.

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OfflineCherk
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Re: Group Theory [Re: Cherk] * 1
    #26982654 - 10/13/20 12:08 AM (3 years, 3 months ago)

zorro bitches!


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I have considered such matters.

SIKE


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OfflineBig_Dub
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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"


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Offlinedark_leviathan
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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.


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OfflineBig_Dub
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Re: Group Theory [Re: dark_leviathan] * 1
    #26994106 - 10/20/20 08:08 AM (3 years, 3 months 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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split_by_nine said:
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InvisibleApostleofAzathoth
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Re: Group Theory [Re: Big_Dub] * 1
    #27445734 - 08/27/21 10:00 PM (2 years, 4 months ago)

Can you define binary?


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OfflineBig_Dub
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Re: Group Theory [Re: ApostleofAzathoth] * 1
    #27445750 - 08/27/21 10:23 PM (2 years, 4 months ago)

Are you asking about the etymology of binary?


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InvisibleApostleofAzathoth
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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?


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OfflineBig_Dub
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Re: Group Theory [Re: ApostleofAzathoth] * 1
    #27445780 - 08/27/21 11:00 PM (2 years, 4 months ago)

It takes two arguments


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split_by_nine said:
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InvisibleApostleofAzathoth
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Re: Group Theory [Re: Big_Dub] * 1
    #27446587 - 08/28/21 04:18 PM (2 years, 4 months ago)

Thanks! Nice thread btw.


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