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 Feb26 awarded Explainer Nov2 awarded Yearling Sep11 comment How to show that $y'(x)=y(x+1)$ is not an ODE? Can you show how to exactly use these to answer the question in the title? Because I still don't see it :p I do now see how $y(x+1)$ is not determined by $x,y(x),\dotsc,y^{(n)}(x)$ but that's not the whole story, is it. Sep11 comment How to show that $y'(x)=y(x+1)$ is not an ODE? @Ian: I'm not very good at analysis, so you have to be more specific. Are you referring to the implicit function theorem? In our definition of ODE, nothing extra is assumed about $F$; it's just a partial function on $\mathbb R^{n+2}$. Sep11 comment How to show that $y'(x)=y(x+1)$ is not an ODE? To use this I guess I would have to find $f$ and $g$ like this which are solutions to the DDE. Then both would be solutions to the proposed ODE $F(x,y(x),\dotsc,y^{(n)}(x))=0$ with the same initial conditions at $x_0$, so $f=g$..? But I don't even have any idea how to prove the existence of these $f$ and $g$. Or is there another way? Sep11 comment How to show that $y'(x)=y(x+1)$ is not an ODE? @Ian: I'm not sure I follow. It seems that you're assuming that every ODE can be expressed in the form $y^{(n)}=f(x,y,y',\dotsc,y^{(n-1)})$, but AFAIK that's not the case. It also seems that even then, the example $z=x^n$ doesn't help because it's not a solution to the given DDE? Sep9 asked How to show that $y'(x)=y(x+1)$ is not an ODE? Sep6 comment Are these proofs logically equivalent? Nah, while I'm fine with someone using non-standard definitions, if they keep coming up I will demand a reference for them before continuing. Sep6 comment Are these proofs logically equivalent? No, the LHS has 1 and the RHS has 2, which is no problem as the equation 1/2 = 1 - 1/2 shows :) Sep6 revised Are these proofs logically equivalent? added 7 characters in body Sep6 answered Are these proofs logically equivalent? Aug19 answered Has the opposite category exactly the same morphisms as the original? Feb23 answered True or false? $(X\setminus Y)\cup(Y\setminus Z)\cup(Z\setminus X) = X\cup Y\cup Z$, for any sets $X$, $Y$, $Z$. Feb9 comment Does the graph of a continuous function have an empty interior? I think you're confusing image with graph. Jan26 answered Class Transitivity Proof Jan14 revised Set theory aspects of category theory added 11 characters in body Jan14 comment Set theory aspects of category theory @ZhenLin Yeah, I was kind of hoping for the converse, so the assumption of the existence of the universe would sound more acceptable, with a proof like "ZFC consistent -> has model -> has transitive model", but I guess the model given by consistency is not necessarily good enough (well-founded) for the Mostowski collapse. Jan14 answered Set theory aspects of category theory Nov2 awarded Yearling Sep5 comment Question on Zorn's lemma dkuper: Bounded chains in $\mathbb Q$ do have an upper bound but may lack a least upper bound.