Thread: Subtraction in F3 Field 1-2-1

Hi,

consider the field

The composition table should look like:

0+0=0
0+1=1+0=1
0+2=2+0=2
1+1=2
1+2=2+1=0
2+2=1

0*0=0=0*1=0*2=1*0=2*0
1*1=1
1*2=2*1=2
2*2=1

No I have the case that I have to calculate:

1-2-1=?

I guess it would be zero but I am not sure

How to do this?

Thank you for helping
greetings

Hello,

1-2-1=(1-1)-2=-2=1

Hi,

first: Thanks for help

second: Could you explain me why this is one? I don't got it

greetings

Originally Posted by Herbststurm

Hi,

first: Thanks for help

second: Could you explain me why this is one? I don't got it

greetings

The fundamental problem with the subtraction operator is that it is NOT ASSOCIATIVE! For example,
Thus parantheses cant be dropped.

So I will interpret 1 - 2 -1 as

Originally Posted by Isomorphism

The fundamental problem with the subtraction operator is that it is NOT ASSOCIATIVE! For example,
Thus parantheses cant be dropped.

So I will interpret 1 - 2 -1 as

Where did anyone mention associativity ?

Originally Posted by Moo

Where did anyone mention associativity ?

Well the problem is how you interpret 1-2-1. Are you thinking of "-" as an operator OR are you thinking of "-x" as a representation for additive inverse?

How do you justify the sequence of operations in your asnwers 1-2-1=(1-1)-2=-2=1?

Originally Posted by Isomorphism

Well the problem is how you interpret 1-2-1. Are you thinking of "-" as an operator OR are you thinking of "-x" as a representation for additive inverse?

How do you justify the sequence of operations in your asnwers 1-2-1=(1-1)-2=-2=1?

Adding the inverse.
Yes, you normally would have to write 1+(-2)+(-1), but this is now how it was stated.
And for simplification, you directly write 1-2-1.

What I did was not using any commutativity of the subtraction. 1-2-1 becoming 1-1-2 is the commutativity of the addition. It's just that it's simplified and not written 1+(-1)+(-2)
After that, it's still associativity, for addition. For the same reasons.