# Tagged Questions

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### What does it mean “sequence with infinite range”

I'm trying to understand this phrase Find a sequence with infinite range that converges only to $0$. What does it mean "sequence with infinite range"? Thanks
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### Terminology: 'inverse' of non-strictly monotonic function?

Suppose I have a nonincreasing function, $x \mapsto f(x) = y$. I want to call the function $$y \mapsto g(y) \triangleq \sup\{x:f(x) \geq y\}$$ the `inverse' of $\ f$ for brevity, despite that $\ f$ ...
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### How to call a function defined on a set with gaps on arbitrarily small scales.

Let $I$ be an interval and $A\subset I$ such that for any two points $x,x'\in A$ there exists an interval $J$ between $x$ and $x'$ such that $J\cap A=\emptyset$. How does one call this proerty of ...
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### Terminology: Alternatives for zero crossing

Is it correct to name the red and blue points hinge points, as an alternative to zero crossing? Or are their better terms to describe these points? Update I have several functions like these. I ...
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### Difference between $C_0^{\infty}(U)$ with support in $A$ and $C_0^{\infty}(A)$

Let $A \subseteq U$ be open sets of $\mathbb R^n$. Is it true that $$\lbrace f \in C_0^{\infty}(A) \rbrace = \lbrace f \in C_0^{\infty}(U) : \text{support of } f \subseteq A \rbrace \quad ?$$ I ...
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### Local topological properties

Could we define the terms locally connected/compact/contractible/simply-connected/whatever to mean that there is a basis (for the topology on our space) of ...
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### Using sequential definition of functional limits, show that $\lim_{x \rightarrow 0} 1/x$ does not exist

Using sequential definition of functional limits, show that $\lim_{x \rightarrow 0} 1/x$ does not exist I have two questions regarding this. Firstly, say we have a function that 'converges' to ...