Talk:Irrational number

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I have suggested that we alter the definition of irrational numbers to "Numbers that can be described by a finite number of integers." Think of the square root of two as an example. There are a number of changes that occur because of this change. For instance: integers and rational numbers become a proper subset of irrational numbers. Irrational numbers become countable and a proper subset subset of continuous numbers. Continuous numbers become the only set of numbers that are not countable. I have entered this before but I need help in handling the requirements dictated by Wikipedia. Should I sign off with :Infinitesets" or Wbaker716 (talk) 17:34, 15 February 2020 (UTC) ?