Index
Russell’s Paradox : The Set that Contains Itself
You are a strange loop.
In 1901, Bertrand Russell discovered a paradox in set theory, a foundational branch of mathematics. Set theory, invented by Georg Cantor in the 1870s, is the study of collections of objects. Sets can contain any objects, regardless of their relation to each other. Russell and other mathematicians believed that numbers could be defined as sets.
Russell’s paradox is a famous paradox in set theory that shook the foundations of mathematics in the early 20th century. It was discovered by the renowned philosopher and logician, Bertrand Russell. The paradox arises when considering the set of all sets that do not contain themselves. Let us dive deep into the discovery and implications of Russell’s paradox.
Imagine a set that contains all the sets that do not contain themselves. Let’s call this set S. Now, we need to ask ourselves, does S contain itself or not?
If S contains itself, then it contradicts the condition of not containing itself that we set out for this set. On the other hand, if S does not contain itself, it satisfies the condition and should be an element of itself. This creates a contradictory situation.