In this document it is shown that the set \(\mathbb{Z}+p\mathbb{Z}\), where \(\mathbb{Z}\) is set of integers and \(p\) is an irrational number, is dense in \( \mathbb{R}\). Not only that but also an equivalent condition that if the set \(\mathbb{Z}+p\mathbb{Z}\) is dense in \(\mathbb{R}\) then \(p\) is irrational. You can directly skip to the article here.

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The article I share here deals with the conceptual complexity and complexity of ideas. It discusses incompleteness theorem and the limitation of the pure thought. How can we formulate this complexity of ideas in terms of mathematical language? Can we even do that? Will a length of an equation determines its complexity? But then again notation changes and with that the form of the equations.

I found this essay involving meta-mathematics, written by Gregory Chaitin, to be interesting and hence, share it here.

Doing Mathematics Differently

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