# What is the set of even numbers?

The set of even numbers is the set of all the numbers that are divisible by 2 (or multiples of 2).

### What are closed numbers?

It depends on what the number is closed on. For example, even numbers are closed on addition. In other words for any two even numbers that are added, the sum is an even number. Numbers are closed if something applies to all the numbers included within a set. The set above includes only even numbers.

### Why are even whole and natural numbers closed under addition?

For a set to be closed under an operation, doing the operations on any two members of the set must result in another member of the set. The set of even natural numbers is {2, 4, 6, ...}. When two even numbers are added, the result is also an even number. Adding two positive numbers results in a larger positive number. Thus, adding two even natural numbers together results in another even natural number and…

### What set of numbers does 4 belong?

Natural (counting) numbers; integers; rational numbers; real numbers; complex numbers. And any other set that you choose to define, that happens to include the number 4 - for example, the set of square numbers, or even numbers, the set of the numbers {3, 4, 5, 7, 14, 48}, etc, the set of numbers containing the letter o in their English name.

### Is intersection of two countably infinite sets can be finite?

Easily. Indeed, it might be empty. Consider the set of positive odd numbers, and the set of positive even numbers. Both are countably infinite, but their intersection is the empty set. For a non-empty intersection, consider the set of positive odd numbers, and 2, and the set of positive even numbers. Both are still countably infinite, but their intersection is {2}.

### Is it true that If A union B equals A union C then B equals C?

NO. The set of numbers in Set B and the set of numbers in Set C CAN be the same, but are not necessarily so. For example if Set A were "All Prime Numbers", Set B were "All Even Numbers", and Set C were "All numbers that end in '2'", A union B would equal A union C since 2 is the only even prime number and 2 is the only prime number that ends…

### What are the different types of set?

In terms of size: the null set, a finite set, a countably infinite set and an uncountably infinite set. A countably infinite set is one where each element of the set can be put into a 1-to-1 correspondence with the set of natural numbers. For example, the set of positive even numbers. It is infinite, but each positive even number can me mapped onto one and only one counting number. The set of Real numbers…