Attempt: $\mathbb{Z}_2\times \mathbb{Z}_2 = \{(0,0),(1,0),(0,1),(1,1)\}$ I tried some examples of a map $f: \mathbb{Z} \to \mathbb{Z}_2\times \mathbb{Z}_2$ such that each element in $\mathbb{Z}_2\times \mathbb{Z}_2$ is mapped by some element, and checked that it wasn't a homomorphism; so I think it doesn't exist. Is this correct? How do I prove this?
2026-04-01 03:43:20.1775015000
Is there a surjective homomorphism from $Z$ to $\mathbb{Z}_2\times \mathbb{Z}_2$?
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