A hyperreal number that is equal to its own integer part
In nonstandard analysis, a hyperintegern is a hyperreal number that is equal to its own integer part. A hyperinteger may be either finite or infinite. A finite hyperinteger is an ordinary integer. An example of an infinite hyperinteger is given by the class of the sequence (1, 2, 3, ...) in the ultrapower construction of the hyperreals.
a hyperinteger n is a hyperreal number that is equal to its own integer part. A hyperinteger may be either finite or infinite. A finite hyperinteger is...
also has sin ( π H ) = 0 {\displaystyle \sin({\pi H})=0} for all hyperintegers H {\displaystyle H} . The transfer principle for ultrapowers is a consequence...
infinitesimal if and only if it is infinitely close to 0. For example, if n is a hyperinteger, i.e. an element of *N − N, then 1/n is an infinitesimal. A hyperreal...
In mathematics, a nonstandard integer may refer to Hyperinteger, the integer part of a hyperreal number an integer in a non-standard model of arithmetic...
st(xn)=L (here the extension principle is used to define xn for every hyperinteger n). This definition has no quantifier alternations. The standard (ε,...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
f(x) = M. ∎ In the setting of non-standard calculus, let N be an infinite hyperinteger. The interval [0, 1] has a natural hyperreal extension. Consider its...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set...
starts with the ring F of finite hyperrationals (i.e. ratio of a pair of hyperintegers), see construction of the real numbers. The quotients R[X] / (X), R[X]...
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