Comments by "" (@jmitterii2) on "Numberphile" channel.

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  4. Mr CJ, I agree with a literal use of 0.  But using it for in equations you discover something interesting about 0, that it has properties that have discrete meanings that have uses: undefined and indeterminate.   Negative numbers do provide lots of understanding that you couldn't do if you took an absolute value, it allows filling geometry with dimensions which dimensions do exist.   Just as complex numbers literally defined are just a place holder, but that place holder works. Complex numbers reveal more of reality.   Infinite sequence segments numbers are also another method that provide detail about physical reality.  Such properties do appear to exist. Our literal absolute number line is only useful for basic everyday uses and even some everyday uses without accepting negative numbers you've just made your life more difficult when coming to liabilities and credit that must be paid sometime in the future. You're just making life harder not to accept these numbers in a more richer way. Otherwise why even bother with real numbers? 1 apple 2 apple real numbers aren't real in that case of literal numbers because each apple is slightly different from another apple.  Even atoms while made of the same amount of protons and neutrons, may have a different energy level in the electron orbitals, etc. And that's not really bringing up all the quantum stuff that describes super positioning, entanglement or uncertainty principle with the wave and particle duality that atom sized objects tend to have. So there isn't any reason to take any of the numbers flat literally. Otherwise you're just making life harder not simpler.   What's important is knowing when to know when such numbers are significant or not to whatever it is you're trying to do with them.
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  10. ***** The law breaks down because it isn't the most accurate model on exactly what is going on. Its wrong for many other conditions. Ohm's Law is only called a law for historical reasons, and since now many stipulate the conditions, its okay to describe Ohm's Law as a Law, but not a model or theory. It incorrectly describes current, voltage, and resistance relationship in conductors for all conditions. It doesn't even work for diodes. People still use it because for normal everyday electronics tend not to be superconductors and aren't working with diodes and other components that violate Ohm's Law.  Or they'll switch away from Ohm's Law. Because it isn't accurate for their use. As for electrical resistance, at the critical temperature, there really is 0 resistance in that material.  While the flaws and vibrations of the atoms do exist, the electrical resistance is 0.  So far tests show even after 50 years the current is still preserved. The atomic flaws and vibrations appear not to interact with the initial current being induced into a superconducting circuit, those flaws and vibrations don't provide any resistance to the current. And current can store forever in the closed system and not violate thermodynamics because no new energy is being created.  Newtonian physics meets Einstein Relativity. One model does good enough job for most things currently, but the other is more accurate and must be used for those conditions requiring its use because Newtonian physics is fundamentally, as a model is wrong for all conditions, Einstein does all of the conditions Newtonian physics allows plus more, so its a more accurate model.  Same with Ohm's Law vs BCS Theory, London Theory, etc. http://www.supraconductivite.fr/en/index.php?p=supra-resistance-supra
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