# Tagged Questions

For questions about the formulation of a proof, not about the mathematics behind it.

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### Prove that $x^3-x = y^2+1$ has no integer solution

Prove that $x^3-x = y^2+1$ has no integer solution: I began the proof by case distinction considering the cases if x,y are both even, if x,y both odd, if x even, y odd and the last one if x odd and y ...
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### Proof on exponential Relation R

Prove that $(R^a)^b = R^{ab}$ for any integers $a,b >= 1$. A handy fact: The connectivity relation $R^*$ consists of the pairs $(x, y)$ such that there is a path of length at least $1$ from $x$ to ...
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### Basic Proofs - If I need to prove (hypothetical) a = b, am I allowed to assume b and derive a? [closed]

Suppose I am trying to prove something that holds for an equality, such as a = b, where a and b can be anything in mathematics. :) Am I allowed to assume b and work towards deriving a? What should be ...
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### A set A is infinite if and only if there is a bijection from the set A to a proper subset of A. [duplicate]

I'm just starting my journey into proof writing and I don't really know how to do this. More specifically I think I want a proof of the fact that every infinite set A is Dedekind-infinite (i.e. that ...
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### proof of continuity of increasing function [duplicate]

Suppose f is an increasing function, with domain D = (a,b). Prove that f is continuous for all except perhaps countably many c in (a,b).
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### Implication vs Equivalence in proofs

I understand the definition of both the implication and equivalence signs. When I get asked to prove something, I will probably have to use both implication and equivalence logic. My question is if ...
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