Closure (mathematics)
Closure in mathematics is when you do an operation like adding, subtraction, multiplying or dividing two numbers and end up with another number that belongs to the same group or set.
Imagine you have a set of numbers, like 1, 2, and 3. If you add any two numbers from this set, you will get another number that is also a part of the set. For example, 1+2= 3, which is already in the set. This set is closed under the operation of addition. This also applies to other operations like subtraction, multiplication, and division.
Closure means that when you perform an operation on elements from a set or group, the outcome is of that same set or group. It helps us verify if a set is valid for the operation we are performing.
So, closure ensures that we don't end up with weird answers that aren't part of the group, and we can fully use the properties that the set has because of its closure under an operation.
Imagine you have a set of numbers, like 1, 2, and 3. If you add any two numbers from this set, you will get another number that is also a part of the set. For example, 1+2= 3, which is already in the set. This set is closed under the operation of addition. This also applies to other operations like subtraction, multiplication, and division.
Closure means that when you perform an operation on elements from a set or group, the outcome is of that same set or group. It helps us verify if a set is valid for the operation we are performing.
So, closure ensures that we don't end up with weird answers that aren't part of the group, and we can fully use the properties that the set has because of its closure under an operation.