Consider a renormalization group (RG) flow triggered at short distances by a relevant perturbation of an ultra-violet (UV) fixed point, and flowing at long distances to an infra-red (IR) fixed point. It may be possible (e.g. in perturbation theory) to monitor how dimensions of UV operators change along the RG flow. In such a situation, one sometimes calls dangerously irrelevant a UV operator whose scaling dimension, while irrelevant at short distances: Δ Δ U V > d , receives a negative correction along a renormalization group flow, so that the operator becomes relevant at long distances: Δ Δ I R < d . This usage of the term is different from the one originally introduced in statistical physics.