- In set theory, a
field of mathematics, the
Burali-Forti
paradox demonstrates that
constructing "the set of all
ordinal numbers"
leads to a contradiction...
-
Paolo Burali d'Arezzo (1511 – 17 June 1578) was an
Italian priest of the
Theatine Order, a bishop, and
cardinal of the
Roman Catholic Church. His legal...
-
within naive set
theory (such as Russell's paradox, Cantor's
paradox and the
Burali-Forti paradox),
various axiomatic systems were
proposed in the
early twentieth...
-
cannot logically exist seems paradoxical to many. This is
related to the
Burali-Forti's
paradox which implies that
there can be no
greatest ordinal number...
-
Cesare Burali-Forti (13
August 1861 – 21
January 1931) was an
Italian mathematician,
after whom the
Burali-Forti
paradox is named. He was a
prolific writer...
- map to A, is a set is not only
Cantorian set but
strongly Cantorian. The
Burali-Forti
paradox of the
largest ordinal number is
resolved in the opposite...
-
could not
itself have a cardinality, as this
would lead to a
paradox of the
Burali-Forti type.
Cantor instead said that it was an "inconsistent" collection...
-
discovered paradoxes in
naive set theory.
Cesare Burali-Forti was the
first to
state a paradox: the
Burali-Forti
paradox shows that the
collection of all...
- not a function, but a function-like class, as it is not a set (due to the
Burali-Forti paradox). For any
ordinal α we have α ≤ ωα. In many
cases ωα is strictly...
- (and to
other similar paradoxes discovered around the time, such as the
Burali-Forti paradox), a
common conception of the idea of set was the "extensional...
