Let $A$ be a subset of the real numbers and $\lambda \in \mathbb{R}$
Then it is claimed that $$\inf_{x\in A}(x+\lambda)=\inf_{x\in A}(x)+\lambda$$
So first of all is this true? Secondly, I have looked at the proof of it here:
https://proofwiki.org/wiki/Infimum_Plus_Constant
and to me it seems like there would be an error in the proof: To go from the formulation in terms of an infimum to a formulation in terms of a supremum they write:
$$\inf_{x\in T}(x+\xi)=-\sup_{x\in T}(-x+\xi)$$
But shouldnt it be $\inf_{x\in T}(x+\xi)=-\sup_{x\in T}(-x-\xi)$ (which of course would make the actual claim in the very first equation false)?