# Mathedu

Learn math by practice

# Re-engineering Math

## 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 furtherâ€¦ 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...

## 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...