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In this paper we review the definition and properties of redundant operatorsin the exact renormalisation group. We explain why it is important to requirethem to be eigenoperators and why generically they appear only as a consequenceof symmetries of the particular choice of renormalisation group equations. Thisclarifies when Newton's constant and or the cosmological constant can beconsidered inessential. We then apply these ideas to the Local PotentialApproximation and approximations of a similar spirit such as the f(R)approximation in the asymptotic safety programme in quantum gravity. We showthat these approximations can break down if the fixed point does not support a`vacuum' solution in the appropriate domain: all eigenoperators becomeredundant and the physical space of perturbations collapses to a point. We showthat this is the case for the recently discovered lines of fixed points in thef(R) flow equations.

Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety