Sequence of real numbers A sequence of real numbers (or a real sequence) is defined as a function $f: \mathbb{N} \to \mathbb{R}$ , where $\mathbb{N}$ is the set of natural numbers and $\mathbb{R}$ is the set of real numbers. Thus, $f(n)=r_n, \ n \in \mathbb{N}, \ # Set Theory, Functions and Real Numbers These study notes on Set Theory, Functions and Real Numbers were written by Gaurav Tiwari when he was studying as a Math undergraduate in 2012-2013. The language is sought to be simple and easy to understand. Further reading material is also provided with this article. If you have any questions, # Numbers – The Basic Introduction If mathematics was a language, logic was the grammar, numbers should have been the alphabet. There are many types of numbers we use in mathematics, but at a broader aspect we may categorize them in two categories: 1. Countable Numbers 2. Uncountable Numbers The numbers which can be counted in # Dedekind’s Theory of Real Numbers Intro Let$ \mathbf{Q}$be the set of rational numbers. It is well known that$ \mathbf{Q}$is an ordered field and also the set$ \mathbf{Q}\$ is equipped with a relation called “less than” which is an order relation. Between two rational numbers there exists an infinite number of

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