0
A paddock is a set that satisfies the 4 addition axioms, 4 multiplication axioms and the distributive law of multiplication and addition but instead of 0 not being equal to 1, 0 equals 1. Where 0 is the additive identity and 1 is the multiplicative identity.
The only example that comes to mind is the set of just 0 (or 1, which in this case equals 0).
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