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I have been wondering about this for some time and thought I would ask here...

It may be a stupid question but I really don't know...

I was wondering if the equations that allow you to calculate things in physics are exactly true, or merely true within a certain error?

For example, take coulomb's law to calculate an electric field:

[tex]E = k \frac{ q_1 q_2 }{r^2}[/tex]

Is there any 'proof' that the '2' in [itex]r^2[/itex] is exactly a 2? Would it be possible that it's actually [itex]r^{2.00000017858726}[/itex] or something?

I understand these things can be verified by doing experiments, but those will tell you the answer to 'only a few' decimals... If experiments verify that the 2 is indeed 2.0000000000, maybe it is infact 2.000000000000000000000018358...

I hope you understand my point...