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Is Zero an Integer? Yes — Here’s Why

You know zero is a rational number. But is zero an integer? To find out, let's review the definition of an integer: A number with no decimals or fractional components. By this definition alone, zero would classify as an integer.

Why Is Zero an Integer?

Integers are any whole numbers (numbers without fractions or decimals) that fall on the number line:

is zero an integer: Number line that shows whole numbers are integers

So along with the above numbers that have positive and negative signs, zero is classified as an integer.

The Complexities of the Number Zero

It’s hard to fit zero into any one set of integers because it’s the only integer that is neither a positive number nor a negative number. Zero also can't be defined as a prime number, which is a positive integer with two positive divisors.

Zero exists as an additive identity element. This means that the sum of adding zero to any number results in the number itself:

is zero an integer: Equation that shows the sum of zero and any number

The inverse of this equation is also true:

Inverse equation of the sum of zero and any number

Similarly, subtracting zero from any number will also result in the number itself:

Equation that shows the difference of zero and any number

Though zero is unique, it still fits into many categories. Zero can be classified as a whole number, natural number, real number, and non-negative integer. It cannot, however, be classified as a counting number, odd number, positive natural number, negative whole number, or complex number (though it can be part of a complex number equation.)

Why You Should Remember Zero's Classification

Knowing that zero is an integer allows you to identify all the other categories that zero can and cannot fit into. Because zero is an integer, it fits into many different algebraic number systems like whole, natural, rational, and real numbers. Zero is also an integral part of the additive identity property, which states that the numeral sum of adding zero to any number is the number itself.

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