# Constructive proof of Herschfeld's Convergence Theorem

## TL;DR

This paper provides a constructive proof of Herschfeld's Convergence Theorem, focusing on transfinite nested radicals and reformulating convergence conditions to enable constructive reasoning.

## Contribution

It introduces a novel constructive proof for Herschfeld's theorem, considering transfinite radicals and new convergence criteria.

## Key findings

- Constructive proof of Herschfeld's Convergence Theorem.
- Extension to transfinite nested radicals.
- Reformulated convergence conditions for constructiveness.

## Abstract

In this paper, we present a constructive proof of Herschfeld's Convergence Theorem. Our formulation differs from Herschfeld's in a few ways: We consider radicals that nest transfinitely many times, as these are essential to the proof; additionally, we formulate the conditions for convergence in such a way that a constructive proof is possible.