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 Jan23 accepted Why implication ($\phi x \Rightarrow \psi x$) is always true according to Russell? Jan23 comment Why implication ($\phi x \Rightarrow \psi x$) is always true according to Russell? Hi @PeterSmith. If I understand T(a) = "if a is human, a is mortal" is a PF of the form $\phi x \Rightarrow \psi x$. Now what Russell says is that T(a) is always true and he is not talking about all of the PFs of the form $\phi x \Rightarrow \psi x$. Am I right? Jan23 asked Why implication ($\phi x \Rightarrow \psi x$) is always true according to Russell? Dec9 accepted What does Russell mean when he defines the “Posterity… with respect to the immediate predecessor”? Dec7 awarded Editor Dec7 revised What does Russell mean when he defines the “Posterity… with respect to the immediate predecessor”? I modified and described my example in two stages Dec7 awarded Supporter Dec7 comment What does Russell mean when he defines the “Posterity… with respect to the immediate predecessor”? Am I wrong when I say that 5 belongs to {0,1,2...}?. Now, since 5 belongs to {0,1,2...} which is hereditary, then {0,1,2...} is the posterity of 5. Dec7 comment What does Russell mean when he defines the “Posterity… with respect to the immediate predecessor”? Thanks @peter. I think that I understand your post, but I still missing something. When Russell says: "all those terms that belong to every hereditary class to which the given number belongs". I need an example. For example given 5. I want to identify the classes that satisfy the definition. After that, identify the members in order to form the posterity. Dec6 comment What does Russell mean when he defines the “Posterity… with respect to the immediate predecessor”? I understand when you say 0 does not belong to the posterity of 5. Please, tell me how did you find the posterity of 5? Dec6 asked What does Russell mean when he defines the “Posterity… with respect to the immediate predecessor”? Apr30 awarded Scholar Apr30 accepted Proof for the funky trace derivative : $d (\operatorname{trace} (ABA'C))$? Apr29 comment Proof for the funky trace derivative : $d (\operatorname{trace} (ABA'C))$? Hi leslie. Now, I understand that proof. Your explanations was very clear. I didn't see matrix calculus and I think the matrix notation was confusing me. Thank you so much. Apr29 awarded Student Apr29 asked Proof for the funky trace derivative : $d (\operatorname{trace} (ABA'C))$?