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# Numbers

Modified 2018-06-22 by Andrea Censi

k:sets

k:naturals, k:integers, k:reals

## Natural numbers

Modified 2018-06-22 by Andrea Censi

$\nats = \{0, 1, 2, \cdots\}$

The natural numbers are the set positive numbers, including zero.

Given two natural their addition is always a natural number:

$$a+b = c \in \nats, \forall a,b \in \nats. \label{eq:intro-nats}\tag{1}$$

The same does not hold of the subtraction operation:

$$a-b = c \in \nats \iff a \geq b.$$

For this reason set of integer numbers is defined.

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