Since [ ] is the greatest integer function we have,Originally Posted bysuedenation

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.

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Thus, this map is not an isomorphism. Think about it, how can you have an isomorphsim between a finite and an infinite set? Impossible.