I know there are differences between the the classical approch and intuitionism and that there are some real numbers in Intuitionism that do not have value (using a weak counterexample). But I want to know if in Intuitionism the real number is the limit of the sequence just as in classical approch (Georg Cantor discoveies using Cauchy sequences).
Does a real number in Intuitionism defined as a limit of a sequence?
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real-numbers
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constructive-mathematics
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1Yes; see Arend Heyting, [Intuitionism : An Introduction](https://books.google.it/books?id=qfp_-Fo9yWMC&pg=PA16) (3rd ed 1971), page 16: **Real number-generators**. – 2017-01-06
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2In intuitionistic logic, the construction of the real numbers via Dedekind cuts and the construction via Cauchy sequences both work but they lead to two different notions of real number. If you come across an intuitionist talking about real numbers, you should always ask him or her which construction they are using $\ddot{\smile}$. – 2017-01-06
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Not always. Quoting a comment above:
In intuitionistic logic, the construction of the real numbers via Dedekind cuts and the construction via Cauchy sequences both work but they lead to two different notions of real number. If you come across an intuitionist talking about real numbers, you should always ask him or her which construction they are using $⌣\hskip-1em¨$. – Rob Arthan Jan 6 at 21:21
(Community wiki answer to an unanswered question.)