A set that contains the elements that is under consideration
In set theory, a universal set is a set which contains all objects, including itself.
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Definition: Universal SetA universal set does not have to be the set of everything that is known or thought to exist - such as the planets, extraterrestrial life, and the galaxies - even though that would be one example of a universal set. A universal set is all the elements, or members, of any group under consideration.For instance, all the stars of the Milky Way galaxy could be a universal set if we are discussing all the stars of the Milky Way galaxy. This type of universal set might be appropriate for astronomers, but it is still a pretty large set of objects to consider.
Milky Way GalaxyA typical universal set we might see in mathematics is the set of natural numbers as shown below:N = {1, 2, 3, 4, …}Boldface capital letters are sometimes used to identify certain number sets, such as N for natural numbers. We usually use braces to enclose a set. The ellipsis mark (…) tells us that the set of natural numbers goes on with no end, so this universal set is also an infinite set. However, universal sets can also be finite sets.Let's look at an example of a universal set that is finite. The set of all the presidents of the United States is an example of a universal set that is finite.