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Old 16th August 2015, 11:34 AM   #384
Giordano
Penultimate Amazing
 
Join Date: Apr 2011
Posts: 17,646
Ironically it is the math that typically matches the reality, as shown by actual experiment and it is the human perception that is often incorrect and does not match the reality. Humans typically don't have an intuitive understanding of relativistic effects, yet GPS confirms that it is the prediction of the math, not the human expectation, that is correct and matches reality in this case. Same for the dual nature of light: it is not that the math fails to explain it, but that we have trouble intuitively understanding it. Again, it is the math that matches the reality as confirmed by experiments. Our perception is incorrect.

I can only reinforce what others here have said: the generating of a repeating string when dividing 1 by 3 is only a problem of the nomenclature, not the math itself. 1/3 is a perfectly acceptable mathematical notation for the precise answer to this division: if you wish instead to express it as a decimal, you must write a bar over the last digit of .3 to use this decimal nomenclature accurately, but it doesn't make either the math itself or the nomenclature incorrect. Different nomenclatures use the same math, but some are more useful than others for given purposes. Fractions for example are easier to write than certain decimals, but harder to use in accounting legers. The nomenclature is just a series of symbols; they are not truly the mathematical concepts that they are meant to indicate.
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