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Sometimes people fail at asking a question by being too broad, unclear like here. So I'll take a stab at what I believe to be the same question, but more concise and clearly stated:

Does infinity exist in either terms of structure, parameters, or measurement in any physical systems?

Can infinity have any real connection with reality?

Or is infinity purely a mathematical concept just used by physicists as a convenient way to describe the very large, an approximation?

I have heard that if you model a physical system (recently Brian Greene posted a video on YouTube regarding infinity), and you run into infinity as a solution, then you have either made an error in your calculations or your model is wrong.

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    $\begingroup$ let $q$ be the charge of the photon, and define $a=1/q$. To all practical purposes, we can say that $a=\infty$. No errors in my model, and it is not wrong, yet I found a physical infinity (or did I?). $\endgroup$ – AccidentalFourierTransform Nov 2 '16 at 19:23
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    $\begingroup$ The infinity of points between zero and one seems pretty real to me, but if you're asking for infinite conserved charges (infinite energy, etc.) that definitely can't be physical. $\endgroup$ – user12029 Nov 2 '16 at 19:25
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    $\begingroup$ Related: physics.stackexchange.com/q/167529/2451 $\endgroup$ – Qmechanic Nov 2 '16 at 19:38
  • $\begingroup$ You say Does infinity exist in either terms of structure, parameters, or measurement in any physical systems Does that include the universe, as a physical system of objects. Please say no :) otherwise, imo, your question is kinda, sort of, just as broad and unclear (no offence intended) as the other guys. $\endgroup$ – user108787 Nov 2 '16 at 21:11
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    $\begingroup$ I suppose that one might meaningfully claim that the conductance (resistance) of a superconductor is infinite (zero). $\endgroup$ – Alfred Centauri Nov 2 '16 at 23:50

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