Definition: Inertial and Noninertial Frames of Reference
Let \(\mathcal R=(\mathbb R,V_{\mathbb R},v)\) be the \(3\)dimensional affine space with the associated normed vector space \((V_{\mathbb R},~)\) over the field of real numbers \(\mathbb R\). Let a frame of reference \(\mathcal I\subset \mathcal R\) contain a massive body \(B\) and let the measurement of its mass be \(m_0\). The frame of reference \(\mathcal I\) is called
 inertial, if consecutive measurements \(i=1,2,\ldots\) of the mass of \(B\) will produce a sequence of measurement values \((m_i)_{n\in\mathbb N}\) deviating from \(m_0\) by less than a fixed (and for the observer negligible error) \(\epsilon > 0\):
\[m_0m_i < \epsilon\quad i=1,2,\ldots,\]
 otherwise \(I\) is called noninertial, i.e. at least one measurement value \(m_j\) will deviate from the error
\[\exists j \ge 1~:~m_0m_j\ge \epsilon.\]
Mentioned in:
Axioms: 1
Definitions: 2
Proofs: 3 4
Propositions: 5 6
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References
Bibliography
 Piotrowski, Andreas: Own Research, 2014