The set of integers divisible by 5 is the set of all integers that result in an integer when divided by 5.
This set encompasses all multiples of 5, including positive integers, negative integers, and zero. We can formally define it as:
{..., -15, -10, -5, 0, 5, 10, 15, ...}
More formally, the set can be represented as:
{n | n = 5k, where k is an integer}
Here's a breakdown:
- Integers: Whole numbers (no fractions or decimals) which can be positive, negative, or zero.
- Divisible by 5: When an integer is divided by 5, the result is also an integer. In other words, the remainder is zero.
Examples:
- 5 is divisible by 5 because 5 / 5 = 1 (an integer).
- -10 is divisible by 5 because -10 / 5 = -2 (an integer).
- 0 is divisible by 5 because 0 / 5 = 0 (an integer).
- 7 is not divisible by 5 because 7 / 5 = 1.4 (not an integer).
Essentially, to determine if an integer is divisible by 5, check if it ends in a 0 or a 5. This provides a quick visual check.
