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Re-engineering Math

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Infinite in Theory, Finite in Practice

When we start to count on our fingers and continue by heart, we only have a small part of all the possible "natural integers": these are all the possible numbers we may count with.

We know that we may count until very very big numbers, the numbers we may imagine, and even further… These very big numbers may be the size of a Galaxy, the size of the known universe, the number of cells in a human body, in all the human bodies, and so on.

The mathematicians construct the set of all "natural...

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Why real numbers are generally not real

The numbers defined in mathematics are in the increasing complexity order:

- The natural integers, from 0 to infinity, that we use to count

- The relative integers, that are the natural integers plus the negative integers, that we use for instance for accountancy "credit" or "debit" notions

- The rational numbers, that we use to share a quantity: they are the result of divisions

- The real numbers, that are all the possible finite or infinite combination of digits, with or without a...

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