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[parent] structure of finite hyperreal numbers (Theorem)

Theorem - Every finite (or limited) hyperreal number $x \in {}^*\mathbb{R}$ admits a unique decomposition of the form

$\displaystyle x = a + \epsilon $
where $a \in \mathbb{R}$ and $\epsilon$ is infinitesimal.

Remark : This theorem just says that every finite hyperreal number has a real part and an infinitesimal part (just like real and imaginary parts in complex numbers).




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Cross-references: complex numbers, imaginary parts, real, real part, finite, infinitesimal, number, hyperreal, theorem

This is version 1 of structure of finite hyperreal numbers, born on 2007-07-28.
Object id is 9810, canonical name is StructureOfFiniteHyperrealNumbers.
Accessed 560 times total.

Classification:
AMS MSC26E35 (Real functions :: Miscellaneous topics :: Nonstandard analysis)

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