a set-theoretic paradox discovered by the British philosopher and mathematician Bertrand Russell in 1901

In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox discovered by the British philosopher and mathematician Bertrand Russell in 1901.

in which a set is defined as containing all sets that do not contain themselves

One of the most famous and absurd recursive Set Theory examples is that of Russell's Paradox, in which a set is defined as containing all sets that do not contain themselves.

The above argument , known as Russell's Paradox

The above argument, known as Russell's Paradox, was discovered by Bertrand Russell in 1901.

the most famous of the set-theoretic paradoxes

Russell’s paradox is the most famous of the set-theoretic paradoxes; the set-theoretic paradoxesarises when one considers the set of all non self-membered sets, the Russell set.

a set-theoretic paradox published by the British philosopher and mathematician Bertrand Russell in 1901

In mathematical logic, Russell's paradox, also known as Russell's antinomy, is a set-theoretic paradox published by the British philosopher and mathematician Bertrand Russell in 1901.

either of two interrelated logical antinomies

Russell’s paradox represents either of two interrelated logical antinomies.

a famous example of an impredicative construction— namely the set of all sets that do not contain themselves

Russell's paradox is a famous example of an impredicative construction—namely the set of all sets that do not contain themselves.

a well-known logical paradox involving self-reference

Russell's Paradox is a well-known logical paradox involving self-reference.

one such concept, , posing a baffling and fundamental challenge to set theoryan area of mathematics concerned with collections of objects

Russell's Paradox is one such concept, posing a baffling and fundamental challenge to set theory, an area of mathematics concerned with collections of objects.

of the self-referential variety

: Russell’s famous paradox is of the self-referential variety.

a barber who is defined such that Bertrand Russell both shaves himself and does not shave himself

Specifically, Russell's paradox describes a barber who is defined such that Bertrand Russell both shaves himself and does not shave himself.

that don't belong to themselves

Russell's paradox arises once we contemplate these units that don't belong to themselves.

us

The explanation is simple, Russell's paradox tells us that there must be some elements whose evaluation doesn't terminate.