# Definition:Strictly Positive/Number

## Definition

The concept of strictly positive can be applied to the following sets of numbers:

$(1): \quad$ The natural numbers $\N$
$(2): \quad$ The integers $\Z$
$(3): \quad$ The rational numbers $\Q$
$(4): \quad$ The real numbers $\R$

### Natural Numbers

The strictly positive natural numbers are the set defined as:

$\N_{>0} := \set {x \in \N: x > 0}$

That is, all the natural numbers that are strictly greater than zero:

$\N_{>0} := \set {1, 2, 3, \ldots}$

### Integers

The strictly positive integers are the set defined as:

$\Z_{> 0} := \set {x \in \Z: x > 0}$

That is, all the integers that are strictly greater than zero:

$\Z_{> 0} := \set {1, 2, 3, \ldots}$

### Rational Numbers

The strictly positive rational numbers are the set defined as:

$\Q_{>0} := \set {x \in \Q: x > 0}$

That is, all the rational numbers that are strictly greater than zero.

### Real Numbers

The strictly positive real numbers are the set defined as:

$\R_{>0} := \set {x \in \R: x > 0}$

That is, all the real numbers that are strictly greater than zero.