Let us consider $C: = \{\lambda \in \text{Card} \ / \ \omega + \lambda = \lambda \}$ (note that we consider here the operations on ordinals and we work in ZFC). I want to prove that $C$ is not a set.
It seems to be an easy question of elementary set theory but I cannot figure out which arguments to use (in general, this kind of question is linked with the Russell's paradox.)
Any hints would be helpful. Moreover what would happened if we took $\lambda \in \text{On}$ ? Will $C$ be a set then ?
Thanks in advance !