# [SOLVED] Functions

• Mar 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.
• Mar 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 $0,1,2,3,4,5,6,7,8,9,10$.
• Mar 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.
• Mar 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 $0,1,2,3,4,5,6,7,8,9,10$.