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I am trying to write all the assumptions or postulates to set up Newton's mechanics:

1.- The space is infinite, continuous, homogeneous, isotropic and 3-dimensional. By this way, we assume that the space can be modeled by $\mathbb{R}^3$

2.- The time is infinite, continuous, 1-dimensional and one-directional.

4.- The space, time and mass are independent concepts

3.- There exits a absolut reference system.

4.- All of the mechanics law are invariante over inertia reference system.

and then, we postulate the three Newton's law.

Some of the above assumptions are the result of the other? which can be omited?

Many thanks.

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    $\begingroup$ Why do you need these infinite spaces? Do you have laboratory data that was taken in an infinite size laboratory? Where did the budget for that physics building come from? Space, time and mass are not independent concepts. One can't define one without the other. There is definitely no absolute reference system, which makes your formulation of the theory 100% false. Newton's three laws exist without any of this mathematical nonsense, but you have to understand the difference between mathematics and physics to know why that is so. $\endgroup$
    – CuriousOne
    Jan 21 '16 at 22:02
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    $\begingroup$ I believe you should add Euclid's Postulates as well, since Newton heavily relies on them in his Principia. $\endgroup$
    – mlg556
    Jan 21 '16 at 22:14
  • $\begingroup$ Assuming space "modeled" as $\mathbb{R}^3$ relies on the "infinite" and "continuous" assumptions, but not on the rest. $\endgroup$
    – Steeven
    Feb 20 '18 at 0:02
  • $\begingroup$ How do you define "inertial frame". Should Galilean invariance be postulate or a result? It seems like it would help to understand why you are interested in this and what you hope to gain. Are you trying to axiomatize physics or understand the relation between empiricism and mathematical abstraction? Just curious. $\endgroup$
    – user196418
    May 30 '18 at 21:27
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I think one key thing you're missing here is the definition of an inertial reference frame, which is really quite tricky to define in the first place. Instead of saying "there exists an absolute reference system," I would say "An inertial reference frame is a frame in which all previous postulates (space is continuous and homogenous, time is infinite and unidirectional, etc.) are satisfied". Another postulate would have to be "All inertial reference frames can be transformed by Galilean transformation to all other inertial reference frames.", otherwise other satisfying the criteria of the previous postulates would be allowed.

In total:

  1. Space is infinite, continuous, homogeneous, isotropic and 3-dimensional.
  2. Time is infinite, continuous, 1-dimensional and one-directional.
  3. Space, time and mass are independent concepts
  4. An inertial reference frame is a frame in which all previous postulates are satisfied.
  5. All inertial reference frames can be transformed by Galilean transformation to all other inertial reference frames.
  6. All laws describing a system are invariant within inertial reference frames.
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