- #26

matt grime

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Mindscrape said:I still don't see why people so readily accept (1/3)=.333~

My take on this is that they think of decimals of representing the answer of doing a division, thus dividing 3 into 1 by long division gives them the sequence 0.3, 0.33, 0.333,... etc, and they somehow think that "thus the result is 0.3....." they do not see such a division for 0.999...

Further, to compound the problem, i suspect that since they do not know what convergence is they only accept 0.333recurring is 1/3 as some kind of decimal 'best guess', thus subconsciously they do not truly think of them as being exactly the same; this is the 'but you never reach the end' argument.

Of course this notional proof of 1/3 times 3 requires that we prove that the algebraic operations on decimals are well defined, which typically is not done.