Russell's Paradox/Also presented as

Russell's Paradox: Also presented as

Russell's paradox can also be presented as:

There is no set $A$ that has every set as its elements.

Its proof follows the same lines: by assuming that such an $A$ exists, and considering the set $\set {x \in A: \map R x}$ where $\map R x$ is the property $x \notin x$.

The same conclusion is reached.


Sources

  • 1999: András Hajnal and Peter Hamburger: Set Theory ... (previous) ... (next): $1$. Notation, Conventions: $6$: Theorem $1.2$
  • 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Russell's paradox
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