Since [ ] is the greatest integer function we have,Originally Posted by suedenation
for all integers.
1)Onto: We need to show that for all we can find such a such as, which is true if you take .
2)One-to-One: We need to show that if then, . Based on the first paragraph that are integers, we have that
3)Homomorphism: We need to show that,
Because, are integers we have,
. Which is definitely not true.
Thus, this map is not an isomorphism. Think about it, how can you have an isomorphsim between a finite and an infinite set? Impossible.