-
always an infinitesimal.
Nonnegative hyperintegers are
sometimes called hypernatural numbers.
Similar remarks apply to the sets N {\displaystyle \mathbb {N}...
- 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...
-
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...
-
international cooperation in Asia and Africa. Machida's
first album Hypernatural (1999) had been
featured with
Brian Eno and Oval (band) on
David Toop's...
-
sequence ( x n ) {\displaystyle (x_{n})}
tends to L if for
every infinite hypernatural H {\textstyle H} , the term x H {\displaystyle x_{H}} is
infinitely close...
- ;\dots d_{\infty -1}d_{\infty }d_{\infty +1}\dots ,}
indexed by the
hypernatural numbers.
While he does not
directly discuss 0.999..., he
shows the real...
- {\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...
- \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...
- Konrad-Adenauer-Stiftung, Berlin,
Germany 2006
Hypernatural,
Centrum Kultury Zamek, Poznan,
Poland Hypernatural,
Galleri Hornbaek, Hornbaek,
Denmark Parallel...
- is a non-standard
model of arithmetic. It can be
identified with the
hypernatural numbers. The
ultraproduct models are uncountable. One way to see this...
