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:
“There are moments when all anxiety and stated toil are becalmed in the infinite leisure and repose of nature.”
—Henry David Thoreau (1817–1862)
“Consider his life which was valueless
In terms of employment, hotel ledgers, news files.
Consider. One bullet in ten thousand kills a man.
Ask. Was so much expenditure justified
On the death of one so young and so silly
Lying under the olive tree, O world, O death?”
—Stephen Spender (1909–1995)
“Before abstraction everything is one, but one like chaos; after abstraction everything is united again, but this union is a free binding of autonomous, self-determined beings. Out of a mob a society has developed, chaos has been transformed into a manifold world.”
—Novalis [Friedrich Von Hardenberg] (1772–1801)
“What a lesson here for our world. One blast, thousands of years of civilization wiped out.”
—Kurt Neumann (1906–1958)