-
always an infinitesimal.
Nonnegative hyperintegers are
sometimes called hypernatural numbers.
Similar remarks apply to the sets N {\displaystyle \mathbb {N}...
-
natural numbers N is not an
internal subset of the
internal set *N of
hypernatural numbers. By
applying the
induction principle for the
standard integers...
- the first-order
Peano axioms) was
developed by
Skolem in 1933. The
hypernatural numbers are an
uncountable model that can be
constructed from the ordinary...
- The
standard part of any
infinitesimal is 0. Thus if N is an
infinite hypernatural, then 1/N is infinitesimal, and st(1/N) = 0. If a
hyperreal u {\displaystyle...
-
whole is
greater than the part". All of this
naturally leads to the
hypernatural numbers. In short,
Benci and his
collaborators propose ****ociating with...
- \mathbb {N} \rangle } has a
natural hyperreal extension,
defined for
hypernatural values H of the
index n in
addition to the
usual natural n. The sequence...
-
continued fraction approximation an of π. Now let the
index n be an
infinite hypernatural number. By the
transfer principle, the
natural extension of the Dirichlet...
- ;\ldots d_{\infty -1}d_{\infty }d_{\infty +1}\ldots ,}
indexed by the
hypernatural numbers.
While he does not
directly discuss 0.999..., he
shows the real...
- Konrad-Adenauer-Stiftung, Berlin,
Germany 2006
Hypernatural,
Centrum Kultury Zamek, Poznan,
Poland Hypernatural,
Galleri Hornbaek, Hornbaek,
Denmark Parallel...
- {\displaystyle a_{H}} of the
natural extension of the
sequence at an
infinite hypernatural index n=H. Thus, lim n → ∞ a n = st ( a H ) . {\displaystyle \lim _{n\to...
