An integer is a whole number that can be either positive, negative, or zero and does not include any decimals. They are formed from counting numbers and subtraction, where subtracting a smaller number from a larger one results in a negative integer and subtracting a number from itself results in zero.

When adding, subtracting, or multiplying integers, the result will always be another integer. However, dividing integers can result in a decimal, such as dividing 5 by 2, which gives 2.5 instead of an integer.

Positive integers are also known as natural numbers. In an equation such as "a + x = b," the solution is only possible if b is greater than a, as both a and x can only be positive, resulting in a larger number when combined. This concept carries over to integers, where this equation will always have an answer.

We can represent integers on a number line, as shown below:

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