Arguments for the continuity principle

@article{Atten2002ArgumentsFT,
  title={Arguments for the continuity principle},
  author={Mark van Atten and Dirk van Dalen},
  journal={Bull. Symb. Log.},
  year={2002},
  volume={8},
  pages={329-347}
}
There are two principles that lend Brouwer's mathematics the extra power beyond arithmetic. Both are presented in Brouwer's writings with little or no argument. One, the principle of bar induction, will not concern us here. The other, the continuity principle for numbers, occurs for the first time in print in [4]. It is formulated and immediately applied to show that the set of numerical choice sequences is not enumerable. In fact, the idea of the continuity property can be dated fairly… 
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