# Definition talk:Real Number

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## Circular problems with the definition using Cauchy Sequences

Many articles about sequences assume we have defined real numbers. Examples: Definition:Convergent Sequence/Note on Domain of N, Definition:Metric Space.

If we don't want to invalidate the construction of $\R$ by Cauchy-sequences, we have to make sure that all definitions and theorems used in its construction do not use $\R$ (better: don't even mention it). This means: when defining an equivalence relation on Cauchy Sequences, this *has* to be done separately for rational numbers. The theorem for general metric spaces can not be used in the construction of $\R$. --barto (talk) 07:49, 28 January 2017 (EST)

- This might be a serious issue. We will have to address this carefully. — Lord_Farin (talk) 04:37, 29 January 2017 (EST)