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Negative Integers

Integers are defined as the numbers which do not have decimal part and are not represented as fractions (though a fraction can be categorized as integer if it has denominator 1). The set of integers is denoted by symbol $\mathbb{Z}$. Integers are of three types: Positive integers, negative integers and zero.

Here, we will study about negative integers.

Negative of all natural numbers are known as negative integers. Negative integers are the integers which are less than zero. All negative integers lie at the left hand side of zero on real number line as demonstrated by following image:

Notation: The set of all negative integers is usually denoted by $\mathbb{Z}^{-}$ and can be defined as illustrated below:

Negative integers do not include zero because these are strictly less than zero. All integers less than zero, i.e. starting from -1 to infinity, are categorized as negative integers. The set of negative integers is the subsets of integers as well as real numbers.

Example: Find the negative integers among the following:
-7, 5, 0.87, 0, -91, $\frac{14}{7}$, 19, -$\frac{11}{1}$, 1.3.
Solution: Since negative integers must have negative sign and must not be written in the form of decimal or fraction,
Therefore , -7, -91 and -$\frac{11}{1}$ (or -11) are negative integers among above numbers.

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