Yes, an integer subtracted by an integer is always an integer.
This is a fundamental property of integers. The set of integers is closed under subtraction. This means that when you perform subtraction on any two integers, the result will invariably be another integer.
Let's break down why:
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Integers: Integers are whole numbers (not fractions) and can be positive, negative, or zero. Examples include -3, -2, -1, 0, 1, 2, 3, and so on.
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Subtraction as addition of the additive inverse: Subtracting an integer is the same as adding its negative (additive inverse). For example, 5 - 3 is the same as 5 + (-3).
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Closure under addition: The set of integers is also closed under addition. When you add two integers, the result is always an integer.
Since subtraction is equivalent to adding the additive inverse, and both the additive inverse and the addition of integers results in an integer, the subtraction of integers will always produce an integer.
Examples:
- 5 - 3 = 2 (Both 5, 3, and 2 are integers)
- (-7) - 2 = -9 (Both -7, 2, and -9 are integers)
- 4 - (-10) = 14 (Both 4, -10, and 14 are integers)
- 0 - 5 = -5 (Both 0, 5, and -5 are integers)
Therefore, regardless of the integers you choose, their difference will always be an integer.
