Definition of Hypernatural. Meaning of Hypernatural. Synonyms of Hypernatural

- 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...
- ;\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...
- 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...
- \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...
- 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...
- {\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...
- 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...
- 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...
- 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...