October 6th, 2018, 01:01 PM  #81  
Senior Member Joined: Jun 2014 From: USA Posts: 422 Thanks: 26 
I am trying to follow your post here. Quote:
$$x \in (0,\infty) \implies \exists y \in \mathbb{R} \text{ such that } y > x$$ Quote:
$$y > x \implies y \in \text{ 'the neighborhood of infinity'}$$ $$x = 1 \implies (1,\infty) = \text{ 'the neighborhood of infinity'}$$ Quote:
The real numbers are already defined. One can define a number in any fashion they see fit, but that doesn't make it a real number. Have you proven that $\infty  b \neq \infty$ and instead that $\infty  b \in \mathbb{R}$ or something? What am I missing...?  

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hypothesis, proof, riemann 
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