# Questions tagged [constructive-mathematics]

The term "constructive mathematics" refers to the discipline in mathematics in which one proves the existence of mathematical objects only by presenting a construction that provides such an object. Indirect proofs involving proof by contradiction and law of excluded middle are considered nonconstructive. Constructivism is the philosophical stance that the only "true" mathematics is constructive mathematics.

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### Example of constructive/intuitionist proof [closed]

I am looking for Examples of constructive/intuitionist proofs I would like to demonstrate a short constructive proof that is simple to explain in about 2 minutes. This is for a presentation about the ...
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### Would this logic be considered constructive?

I have asked about similar logics before, but this one is different. The logics that I’ve asked about in the past take the Gödel-McKinsey-Tarski translation for Intuitionistic Propositional Logic to ...
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### Different Notions of Maximal Ideals in Constructive Mathematics?

I was working on proving the following classic result for non-zero commutative rings in constructive logic: $I \subseteq R$ is a maximal ideal iff $R / I$ is a field. The definition of maximal ...
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### Transfering colored balls from random bags into identical ones

Let's consider the following scenario: There are $n$ colors, and there are $n^2$ colored balls, where we have $n$ balls of each of the $n$ colors. There are also $n$ bags $[b_1,b_2,\dots,b_n]$ where ...
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### How to prove that a formula is intuitionistically valid using Kripke semantics?

I want to know how to use Kripke semantics so that I can prove that a formula is intuitionistically valid. I think that all others cases will clear out if I understand the case of implication. Let's ...
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### Is $\sqrt{2}^{2\log_2 3} = 3$ a constructive solution?

$\sqrt{2}^{2\log_2 3} = 3$ is a solution to Can an irrational number raised to an irrational power be rational? While the famous $\sqrt{2}^{\sqrt{2}}$ proof is nonconstructive, this one is apparently ...
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### Intuitionistic well-orderings of uncountable sets

The well-ordering principle has always been considered to be highly unconstructive, as far as I know. However, I think intuitionistic mathematics can be compatible with the existence of a well-...
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### Well-Ordering Principle From Recursion Theorem

As far as I understand, in intuitionistic logic we have neither (i) the well-ordering principle nor (ii) the recursion theorem. But can one deduce one from the other? I believe we cannot deduce (ii) ...
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### Why is the Principle of Explosion considered constructive?

I read over this post Why is the principle of explosion accepted in constructive mathematics? and still have some thoughts/questions. One of the answers mentions that a formula is constructively valid ...
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### Proving the Existence of a Number without Constructing

Prove that for all $k \in \mathbb{N}$ then there exists $n$ such that $$7^k \mid 2^n + 5^n + 3$$ My idea is to construct $n$ such that the equation above is valid. However, the construction that I ...
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