# Improved Definition of NonStandard Neutrosophic Logic and Introduction to Neutrosophic Hyperreals

## TL;DR

This paper refines the definition of NonStandard Neutrosophic Logic, introduces Neutrosophic Hyperreals, and discusses their theoretical foundations, practical applications, and critiques prior work and misconceptions in the field.

## Contribution

It provides an improved formal framework for NonStandard Neutrosophic Logic and introduces Neutrosophic Hyperreals, addressing previous limitations and misconceptions.

## Key findings

- NonStandard Neutrosophic Logic was never practically used in applications.
- Neutrosophic Hyperreals are indeterminate and lack a total order.
- Transfer principle in hyperreals is questionable due to indeterminacy.

## Abstract

O the third version of this response-paper to Imamura criticism, we recall that NonStandard Neutrosophic Logic was never used by neutrosophic community in no application, that the quarter of century old neutrosophic operators (1995) criticized by Imamura were never utilized since they were improved shortly after but he omits to tell their development, and that in real world applications we need to convert/approximate the NonStandard Analysis hyperreals, monads and binads to tiny intervals with the desired accuracy, otherwise they would be inapplicable. We point out several errors and false statements by Imamura with respect to the inf/sup of nonstandard subsets, also Imamura 'rigorous definition of neutrosophic logic' is wrong and the same for his definition of nonstandard unit interval, and we prove that there is not a total order on the set of hyperreals (because of the newly introduced Neutrosophic Hyperreals that are indeterminate), whence the transfer principle is questionable.

---
Source: https://tomesphere.com/paper/1812.02534