In this notation, how do you define a linear function g? Generalize λ,z∈ℝ to more general fields or vector spaces, as appropriate.

In the given notation, a linear function \(g: \mathbb{R} \to \mathbb{R}\) (or more precisely, a function that is homogeneous of degree 1, which is the scalar multiplication aspect of linearity) would be defined by negating the existential quantifier and inequality from the original statement. Specifically: \[ \forall \lambda, z \in \mathbb{R}: \, g(\lambda z) = \lambda g(z) \] This means

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