# 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) $$\epsilon > 0$$: $|m_0-m_i| < \epsilon\quad i=1,2,\ldots,$
• otherwise $$I$$ is called non-inertial, i.e. at least one measurement value $$m_j$$ will deviate from the error $\exists j \ge 1~:~|m_0-m_j|\ge \epsilon.$

Axioms: 1
Definitions: 2
Proofs: 3 4
Propositions: 5 6

Github: ### References

#### Bibliography

1. Piotrowski, Andreas: Own Research, 2014