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Groups/ binary ops

Hi guys,

Im having some trouble with a practice question, i was wondering if anyone could help me out.
here it is:
Let T = {0,1,2}
i) How many binary operations * can you define on T?

I dont even know where to start
Thanks in advance
What do you think the question is asking? what do you know about binary operations?
Reply 2
Avatar for tsmith16
tsmith16
OP
Your advice is ringing bells but i dont really know where there going

Sorry if im being silly,
Thanks for the reply
Original post by tsmith16
Your advice is ringing bells but i dont really know where there going

Sorry if im being silly,
Thanks for the reply


Consider all the possibilties basically is what he is saying!
Reply 4
Avatar for nuodai
nuodai
17
This isn't necessarily the best thing to do if {0,1,2} is a group under * (which I assume is the case given the thread title) and not just a set with a binary operation.

My advice would be: you have a choice over which element is the identity; do you have a choice over what the other two elements can do?
(edited 13 years ago)
Reply 5
Avatar for DFranklin
DFranklin
18
Original post by nuodai
This isn't necessarily the best thing to do if {0,1,2} is a group under * (which I assume is the case given the thread title).You know what they say about assumptions.

(The question has been posted before over the last few days - it's definitely "how many binary operations" as the 2nd part is "how many groups").
Reply 6
Avatar for nuodai
nuodai
17
Original post by DFranklin
You know what they say about assumptions.

Alas, indeed.
Reply 7
Avatar for DFranklin
DFranklin
18
Original post by nuodai
Alas, indeed.
To be clear, it wasn't unreasonable, but given I'd seen the previous thread I was pretty sure it wasn't the right path here.
Reply 8
Avatar for tsmith16
tsmith16
OP
hmmm, its making abit more sense, sorry its been a while since i've seen binary ops, can you give me one example to kick start me?
thanks again, i know how frustrating this can be
Reply 9
Avatar for tsmith16
tsmith16
OP
Do you guys want me to post part (ii) of the question?
Reply 10
Avatar for tsmith16
tsmith16
OP
Original post by nuodai
This isn't necessarily the best thing to do if {0,1,2} is a group under * (which I assume is the case given the thread title) and not just a set with a binary operation.

My advice would be: you have a choice over which element is the identity; do you have a choice over what the other two elements can do?


Hi, are there 18 binary ops that can be defined on T? I've done a little more research and i've come up with:

(0*1,0*2,1*0,1*2,2*0,2*1), all of which have three options, giving 18 bin ops.

ps, can i have a a pair (0*0) or (1*1) or (2*2)?
EDIT: ive assumed, (i think correctly) that i can use (1*1) and (2*2), but im not sure if i can use (0*0) because you cant do get any other number other than 0 given any binary operation with the pair (0*0).

Thanks
(edited 13 years ago)
Reply 11
Avatar for tsmith16
tsmith16
OP
hey :smile:,
i think youve got the main point of my question, is there 3^(3^2) arbitrary binary ops on any set of 3 elements, giving 19,683 bin ops on T?
thanks

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