[SOLVED] Functions

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March 2nd 2009, 05:53 PM
ronaldo_07

[SOLVED] Functions

http://img25.imageshack.us/img25/1862/algebra.jpg

How to determine this and please provide explanation if possible.
March 2nd 2009, 06:08 PM
GaloisTheory1

Quote:

Originally Posted by ronaldo_07

http://img25.imageshack.us/img25/1862/algebra.jpg

How to determine this and please provide explanation if possible.

a. not $1-1$ , ie $1 \mapsto 1$ and $2 \mapsto 1$
b. yes, it is $1-1$ , easily can be checked, check $0,1,2,3,4,5,6,7,8,9,10$ .
March 2nd 2009, 06:12 PM
ronaldo_07

Thank you could you explain it a bit further if possible please, how can you tell that 1 maps to 1 and 2 maps to 1.
March 3rd 2009, 10:28 AM
GaloisTheory1

Quote:

Originally Posted by GaloisTheory1

a. not $1-1$ , ie $1 \mapsto 1$ and $2 \mapsto 1$
b. yes, it is $1-1$ , easily can be checked, check $0,1,2,3,4,5,6,7,8,9,10$ .

sure. a. not $1-1$ , ie $1 \mapsto 1$ and $2 \mapsto 1$ b/c $1^3=1 \in \mathbb{Z}_7$ and $2^3=1 \in \mathbb{Z}_7$

not onto. check $0,1,2,3,4,5,6$

b. yes, it is $1-1$ , easily can be checked, check $0,1,2,3,4,5,6,7,8,9,10$ .

yes, it is onto. check $0,1,2,3,4,5,6,7,8,9,10$ .

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