-- | Finite nimber addition is calculated as follows: the nimber sum of a two-power and itself is 0, while the nimber sum of two distinct two-powers is their ordinary sum.
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--   Finite nimber multiplication is calculated as follows: the nimber square of a Fermat two-power is its sesquimultiple, while the nimber product of two distinct Fermat two-powers is their ordinary product.
--   The sesquimultiple of a Fermat two-power is equal to itself plus the product of all smaller Fermat two-powers.
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--  @'abs'@ and @'signum'@ don't really make sense for nimbers.  They are defined as @'id'@ here.

  -- \| Finite nimber addition is calculated as follows: the nimber sum of a two-power and itself is 0, while the nimber sum of two distinct two-powers is their ordinary sum.

  -- \| Finite nimber multiplication is calculated as follows: the nimber square of a Fermat two-power is its sesquimultiple, while the nimber product of two distinct Fermat two-powers is their ordinary product.