Infinity Computer Arithmetic Logic Unit Infinite Radix System
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Solution Overview
Problem
Current computer systems are unable to perform arithmetic operations with infinite and infinitesimal numbers in the same manner as they handle finite real numbers, due to the complexities and uncertainties associated with such operations, such as infinity minus infinity or infinity divided by infinity, which are often left undetermined or represented using infinite sequences of finite numbers.
Innovation Solution
A new type of computer, referred to as the 'infinity computer,' is developed to operate with infinite, infinitesimal, and finite numbers by introducing a new positional system with an infinite radix, allowing for the storage and arithmetic logic unit (NALU) to execute operations with these numbers. This system organizes memory and defines arithmetic operations for all types of numbers, enabling standard arithmetic operations across all number types.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional computer systems use standard arithmetic operations with finite numbers, then computation is straightforward and well-defined, but they cannot handle infinite and infinitesimal numbers
Solution Approach 1:
The patent changes the fundamental parameter of the numeral system by introducing an infinite radix (base) system. This allows the computer to represent and manipulate infinite and infinitesimal numbers directly, rather than using finite approximations. The infinite radix system provides a consistent framework where arithmetic operations on infinite numbers yield deterministic results, resolving the contradiction between versatility and reliability.
2Quantity of substance
If computers represent infinite numbers using infinite sequences of finite numbers, then infinite numbers can be stored, but arithmetic operations become complex and often undetermined
Solution Approach 1:
Instead of representing infinite numbers as sequences of finite numbers (the conventional approach), the patent inverts the approach by using an infinite radix system where infinite numbers are represented directly and naturally. This inversion simplifies arithmetic operations because the infinite radix provides a consistent place-value system that handles infinite numbers the same way finite radix systems handle finite numbers, eliminating the need for complex sequence-based arithmetic.
3Ease of operation
If a new positional system with infinite radix is introduced, then arithmetic operations with infinite numbers become straightforward, but the system complexity increases
Solution Approach 1:
The infinite radix positional system serves multiple functions: it can represent finite numbers, infinite numbers, and infinitesimal numbers using the same consistent framework. This universality means that the same arithmetic rules and operations apply to all three types of numbers, simplifying the overall system design despite the increased conceptual complexity of handling infinite radices. The system achieves ease of operation through this unified approach.
Data Source
AI summary
In this invention we describe a new type of computer—infinity computer—that is able to operate with infinite, infinitesimal, and finite numbers in such a way that it becomes possible to execute the usual arithmetical operations with all of them. For the new computer it is shown how the memory for storage of these members is organized and how the new arithmetic logic unit (NALU) executing arithmetical operations with them works.