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ZFC is relatively consistent to ZF. The same is true for ZF and ZF without the Axiom of Foundation. Are there answers to similar questions, like the relative consistency of the Axiom of Infinity to some “lower” set of axioms? Or are there even papers which proof the relative consistency of ZF to the AxiomRead more

I know asking for proof-verification on MO is a tricky thing. On one hand interesting research level proofs are usually subject of articles and can not be discussed here in detail. On the other hand most simple proof which can be written on a forum are not “high-level” enough for MO and other places areRead more

In my study I need to construct a holomorphic function with the following property. Can anyone help with an idea? Showing the existence or non-existence is far good. Let $ D:=\left\{ z\in\mathbb{C}:0<\left|z\right|<1\right\} .$ Is it possible to construct a holomorphic function $ F:D\rightarrow\mathbb{C}$ such that $ $ \left|z\right|^{-\frac{1}{3}}\leq\left|F\left(z\right)\right|\leq\left|z\right|^{-\frac{1}{2}}, $ $ for any $ z\in D?$Read more

Maybe this is a trivial question. But I do not find any thing about it in my searching in the net. Let us consider the elliptic curve $ $ y²=x³+ax+b$ $ where $ a,b$ are integers. My question is about the existence of a single singular bijective function $ f(t,a,b)$ verifying $ $ x=f^{(1/3)}(t,a,b)$ $Read more

I’m looking for existence results for the equation $ $ \lambda u-\frac{1}{(1+(u’)^2)^2} \, \Delta u = f \quad \text{on the domain $ [a,b]$ }$ $ for $ u:[a,b] \to \mathbb{R}$ , with either zero Dirichlet or Neumann BCs. Here $ f$ is some data, but preferably some results on $ f=f(u)$ nonlinear and smooth wouldRead more

They claim David Duke is a liberal. If that’s true, I guess OJ Simpson is a white man. If David Duke is a liberal, that also mean that the Kardashians possess talent. If David Duke is a liberal, that also must mean Stephen Curry is helping the New England Patriots keep their Super Bowl hopesRead more

I’ve two apps, A & B. When I start app A, it prompts me with a message: “Please remove app B to continue!” How can I prevent app A from reading the installed apps list. Or is there a way to rename app B to something else? App A is a taxi app like Ubber.Read more

Is the “dark and stormy lab” in which Dennis Richie and Ken Thompson developed Unix still in existence and preserved as of the end of 2017? I might take a trip to USA someday and go visit that lab. Better than some museums for me I would guess. Note: I took the term “dark andRead more

Let $ X$ be a separable metrizable connected space. Question. Does $ X$ necessarily have a subset $ D$ such that $ \overline D=X$ and $ X\setminus D$ is a connected set with more than one point? This seems “obviously true” to me but I have not been able to prove it.Read more

Lets say temporarily that a topological space $ (X,\tau)$ is weird if there is a function $ \varphi:X \to \tau$ such that for all $ x \in X$ : $ x\in\varphi(x)$ , $ \{y\in X: x \in \varphi(y)\}$ is finite. A function satisfying the first condition is sometimes called a neighborhood assignment. Note that discreteRead more