Are there higher levels of infinity?

Are there higher levels of infinity?

Infinity is a powerful concept. There are actually many different sizes or levels of infinity; some infinite sets are vastly larger than other infinite sets. The theory of infinite sets was developed in the late nineteenth century by the brilliant mathematician Georg Cantor.

What are the levels of infinity?

Each of these was further subdivided into three orders:

• Enumerable: lowest, intermediate, and highest.
• Innumerable: nearly innumerable, truly innumerable, and innumerably innumerable.
• Infinite: nearly infinite, truly infinite, infinitely infinite.

How many different sizes of infinity are there?

There are actually many different sizes or levels of infinity; some infinite sets are vastly larger than other infinite sets. The theory of infinite sets was developed in the late nineteenth century by the brilliant mathematician Georg Cantor.

What is the baseline level of Infinity?

An icon in the shape of a lightning bolt. Our baseline level of infinity will come from our most basic infinite set: the previously mentioned natural numbers. A set that is the same size as the natural numbers — that can be put into a one to one correspondence with the natural numbers — is called a countably infinite set.

What is Cantor’s theory of infinity and infinite sets?

Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.

What is infinity in math?

Infinity is also an extremely important concept in mathematics. Infinity shows up almost immediately in dealing with infinitely large sets — collections of numbers that go on forever, like the natural, or counting numbers: 1, 2, 3, 4, 5, and so on.