##### Numerical Infinity and

## The Infinity Computer

#### The problem

- Nowadays physical limits (speed, miniaturization) of traditional computers have been almost reached. Current attention of the industrial and scientific communities is dedicated to new computational paradigms and areas of their possible applications.
- In spite of huge investments, there do not exist on the market general purpose unconventional computer architectures ready for a broad implementation and production. For instance, industrial quantum general purpose computers do not exist (D-Wave is not general purpose).
- Traditional computers work with finite numbers only. Numerical computations with infinities and infinitesimals are impossible due to: 1. the presence of indeterminate forms such as ∞ – ∞, ∞ / ∞, ∞ · 0. 2. the impossibility to put infinite numbers in the finite computer memory.
- There exists an insuperable wall in performance beyond which traditional computers are not able to go and all kinds of divergences and usage of infinitesimals can be studied only analytically by human beings.

#### Grossone® Infinity Computer

The Infinity Computer is a new kind of a supercomputer able to execute numerical computations with finite, infinite, and infinitesimal numbers using a new numeral system with the infinite radix called Grossone® and expressed by the symbol ⓵

- An analogy: Ancient Romans did not know about existence of zero and negative numbers. As a consequence, they were not able to execute computations requiring these numbers and such expressions as V-V or III-X were indeterminate forms for them. In modern computations 0 is indispensable and the work of traditional computers is impossible without zero and negative numbers.
- The Infinity Computer makes a similar thing thanks to Grossone® making possible the passage from finite numbers to infinities and infinitesimals and allows consumers to work numerically with different infinities and infinitesimals as with finite numbers giving so to the consumers an unprecedented level of accuracy and power of computations that does not exist on the market.