Hello! I have a problem with one proof. The task is: Suppose that X is linear space, x belongs to X and λ is real number. Proof if λx=0 so λ=0 or x=0. And there are conditions. Can use only this properties μ also is real number: I tryed to prove that but completely fails. Let λ=0. According to d, λx=0 Let x=0. From c and g => λ(0+0)=λ0+λ0. And then i dont know what to do next. And also i think need to prove that if λ and x is not equal to zero when the product of them also not equal to zero. Thanks for helping!