Definition:Strictly Positive/Number
< Definition:Strictly Positive(Redirected from Definition:Strictly Positive Number)
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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.