Stated in Terms of Von Neumann Ordinals
The reason is that the set of all ordinal numbers carries all properties of an ordinal number and would have to be considered an ordinal number itself. Then, we can construct its successor, which is strictly greater than . However, this ordinal number must be an element of since contains all ordinal numbers, and we arrive at:
- and
Read more about this topic: Burali-Forti Paradox
Famous quotes containing the words stated, terms, von and/or neumann:
“May something go always unharvested!
May much stay out of our stated plan,
Apples or something forgotten and left,
So smelling their sweetness would be no theft.”
—Robert Frost (18741963)
“Ive never been on good terms with God, but now Im becoming His intimate, for He is truly absolute and extremely legitimate.”
—Franz Grillparzer (17911872)
“Everything in science depends on what one calls an aperçu, on becoming aware of what is at the bottom of the phenomena. Such becoming aware is infinitely fertile.”
—Johann Wolfgang Von Goethe (17491832)
“What a lesson here for our world. One blast, thousands of years of civilization wiped out.”
—Kurt Neumann (19061958)