# Questions tagged [constructive-mathematics]

In constructivism, an existence proof is not accepted, unless the object in question is constructed. Also, the law of excluded middle is typically not accepted as an axiom.

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### Is there a game semantical countermodel to Markov's Principle?

For specificity, let's fix Markov's Principle as $$\forall P : \mathbb N \to 2. \neg(\forall n : \mathbb N. P(n) = 0) \to \exists m : \mathbb N. P(m) = 1.$$ I've seen an informal argument that this ...
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### Piecewise linear functions in constructive mathematics

Is is possible to constructively prove that, for any function $f:\mathbb{R}\to\mathbb{R}$ piecewise linear, the absolute value $|f|:\mathbb{R}\to\mathbb{R}$ is also piecewise linear ? "Constructively"...
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### The price of constructivity

It is said that proofs in constructive math, if possible at all, tend to be more verbose than in classical math. I'm trying to get an intuition for this, so: Are there any good example of theorems ...
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### Is real analysis constructive?

I'm still wrapping my head around exactly what 'constructive' mathematics is. To my understanding, there are several theorems in real analysis which depend on the axiom of either dependent or ...
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### Constructivity and Piecewise Functions

I'm currently exploring homotopy type theory and intuitionistic mathematics. In constructive/intuitionistic mathematics, 2 features arise: A proof of $\neg \neg A$ is not a proof of $A$. All ...
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### How to construct a sequence that is the set of limit points but not equal to any element in another sequence?

Let ${y_j}_{j=1}^N$ be N given real numbers. Construct a sequence ${a_n}$ so that ${y_j}_{j=1}^N$ is the set of limit points of ${a_n}$, but $a_n \ne y_j$ for any n or j. My work is as follows, but ...
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### Why is the principle of explosion accepted in constructive mathematics?

I think something is wrong with the principle of explosion, because according to it, if I know $P\wedge \lnot P$, I can deduce $Q$ though I don't know anything about $Q$. Is it really constructive to ...
I have two real numbers $x,a$ and I know that $\vert 1 - t \vert > 0$, where $t > 0$. Then I have \begin{align*} \Vert tx + (1-t)a\Vert = \Vert 1- t \Vert \Vert \frac{t}{1-t} x - a\Vert. \end{...