Is the existence of transcendental numbers an actual existence?

Contents

1. Introduction
   1. The potential and the actual existence
   2. The intensive and the extensive infinite
2. The new concept of qualitative infinity
3. Duality of extensive and intensive infinity in qualitative infinity
4. The actual existence of transcendental numbers
   1. The actual existence of transcendental numbers in positional numeral systems
   2. The actual existence and geometry
   3. Continuity and infinity
   4. An artificial intelligence (AI) answer to the question of the actual existence of transcendental numbers
5. The idealization of "arbitrarily large finite" with potential infinity
6. Summary

Appendix A- Elementary properties of two-element numbers
Appendix B - Two-element numbers and homogeneous coordinates
Appendix C - Axiomatisation of set theory with the new qualitative infinite

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