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A Function $g[0,\infty) \mapsto [0,1)$ Sharply Changing on Both Ends [closed]

I need a function $g[0,\infty) \mapsto [0,1)$ that sharply decreases near 0 and sharply increases near 1. Preferably, it wouldn't be defined in a piecewise manner. Can anyone provide an example, ...
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Direct construction of the integers

Is there a direct construction of the integers which does not involve taking any quotients? I am of course aware of the usual construction. I am also aware of the nice axiomatic characterization of ...
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reduced ⊗ reduced = reduced; what about connected?

Several questions actually. All rings and algebras are supposed to be commutative and with $1$ here. (1) Let $k$ be a field, and let $A$ and $B$ be two $k$-algebras. I need a proof that if $A$ and ...
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Axiom of choice and convergence

Hi fellows, I was wondering. Is the axiom of choice used to show that $\mathbb{R}$ is complete? If yes, is there a way to construct monotonic bounded sequences that do not converge? Thanks in ...
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Maximum sum of 3 consecutive numbers in a permutation [closed]

Given that $X = \{0, 1, 2, ..., 7, 8, 9\}$, and $P$ is a permutation on $X$. Let $M(P)$ be the maximum sum of 3 consecutive elements. For example, if $P = (0, 2, 4, 1, 5, 7, 9, 3, 8, 6)$, then $M(P)$ ...
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Are there any mathematical objects that exist but have no concrete examples? [closed]

I am curious as to whether there exists a mathematical object in any field that can be proven to exist but has no concrete examples? I.e., something completely non-constructive. The closest example ...
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Intuitionistic Lowenheim-Skolem?

Is there a version of the Löwenheim-Skolem theorem in intuitionistic logic? I'm particularly interested in the "downward" form. The standard proof I know uses the Tarski-Vaught test for ...
729 views

Are all group monomorphisms regular, constructively?

By "constructive" I mean something that would go through in CZF for example. [added Oct 6] A sketch of a standard proof (such as referenced in comment below), which is almost constructive: Let H be a ...