bijective

• Nov 9th 2008, 05:13 AM
math_lete
bijective
Hey i have a question
f:X--->Y
X=Z(integers) Y={1,2,3}*Z(integers)

i have to find a bijective map. So obviously i prove it is injective amd surjective. However i am confused about how because my examples in my notes are different to this. They all give an f(X) Function whereas this does not.
• Nov 9th 2008, 05:19 AM
Plato
Quote:

Originally Posted by math_lete
Hey i have a question
f:X--->Y
X=Z(integers) Y={1,2,3}*Z(integers)

If by {1,2,3}*Z you mean $\{ 1,2,3\} \times \mathbb{Z}$ then try to show that
$\phi :\mathbb{Z} \mapsto \{ 1,2,3\} \times \mathbb{Z}\;,\;\phi (z) = \left( {\bmod (z,3) + 1,\left\lceil {\frac{z}{3}} \right\rceil } \right)$ is a bijection.