The continuum is a range, series, or spectrum that slowly changes. It can be a physical range, such as the seasons or a biological range, such as human fertility. It can also be a cultural range, such as gender expectations or social classes.
The word continuum comes from the Latin continuum, meaning “a continuous line or range,” and it is defined as “a continuous series of things” (Cambridge Dictionary). It can be described as a set of items that are similar to one another but have differences to a degree.
In the sciences, it can describe the flow of fluids and the movement of bodies in space. It can also be used in mathematics to explain the behavior of objects in motion, such as planets and stars.
Continuums are also important in the arts, such as music. For example, a song might start at a high point and then gradually fade away, as the artist continues to progress toward the end of the album.
It is a common theme in science fiction novels, as well as movies. It has been used in the films The Matrix and Avatar, as well as in the television show Stargate SG-1.
In physics, the continuum is used to model many processes in nature. It is a useful tool in solving many problems, including the evolution of galaxies.
During the 1930s, Kurt Godel began to focus on the problem of the continuum hypothesis. He was a mathematician and philosopher who worked in many areas of mathematics and philosophy, including set theory.
Although he was a relative newcomer to the problem, he soon became involved in its development. He was responsible for a number of important developments in the history of the continuum hypothesis.
First, he was able to prove that the continuum hypothesis holds for a particular class of sets called Borel sets. This is a concrete class of sets, with for the most part the same properties as the usual set theory sets that we work with.
Later, he was able to show that the same principle applies to larger and larger sets, as well as more complicated mathematical models.
As a result, the solvability of the continuum hypothesis was becoming an increasingly popular topic among set theorists. This was especially true after several key new principles from conceptually quite different areas were shown to imply that the size of the continuum is 2.
These results were followed by other new developments, and in some cases the problem was finally solved. In the 1990s, for example, a group of mathematicians from the University of Minnesota, led by David Shelah, was able to show that the continuum hypothesis is provably fixed for infinite cardinals in a certain class of mathematical spaces.
Then, a few years ago, a team of researchers from the Institute for Advanced Study in Princeton, led by Jorg Brendle and Paul Larson, showed that the same principle also explains why the continuum hypothesis is provably fixed in ZFC, the set of real numbers.