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> He asked me why 1/3 + 1/3 + 1/3 = 1, since it's equal to 0.333... + 0.333... + 0.333... which is 0.999... How can that possibly equal 1.000...? And is 0.66...
by rudolph9 6y ago
> He asked me why 1/3 + 1/3 + 1/3 = 1, since it's equal to 0.333... + 0.333... + 0.333... which is 0.999... How can that possibly equal 1.000...? And is 0.66... equal to 0.67000...?
This would make me very proud.
- boxy310 6y agoYes, it's quite clever. An equivalent proof is dividing 0.999... by 9 using long division, which comes out to 0.111... which is equal to 1/9. Now use fraction notation and it simplifies to 9/9 = 1. Not quite as robust as the limit-based proofs but it's a quick answer and gets to the heart of the issue of repeating notation not capturing the whole picture.