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Authored by: Anonymous on Friday, December 14 2012 @ 12:47 PM EST |
When you square both sides, you introduce a new possible solution. Same for
roots. Dividing by a variable reduces your solution set to x>0 or x<0,
your choice. You can play lots of games using correct steps, but failing to get
the math right.
Things get really iffy at infinity. But everything I know says that 3*(1/3) =
1. A decimal expression of 1/3 is 0.333... Just because our decimal
representation is flawed does not make 3*(1/3) anything other than unity. So
yes, 0.999... = 1. Because of an artifact of decimal representation.
-- Alma[ Reply to This | Parent | # ]
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Authored by: Anonymous on Friday, December 14 2012 @ 01:00 PM EST |
Sorry, the fallacy is in the square step.
I'm more inclined to go via:
let x = 0.999... [1]
Then:
10x = 10 x 0.999... = 9.999... [2]
Subtract equation 1 from 2:
[2] - [1]: 10x - x = 9.999... - 0.999...
→ 9x = 9 (the recurring decimal parts are exactly the same and
subtract to leave just the whole number)
→ x = 1 (divide both sides by 9).
[ Reply to This | Parent | # ]
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Authored by: ukjaybrat on Monday, December 17 2012 @ 01:18 PM EST |
When you first equate something and then it turns out fine
does
not mean it is
correct.
i didn't start off with an eroneous
statement that turned out
fine "1/9 = 0.111..." is a factual statement, unlike
"4=6"--- IANAL [ Reply to This | Parent | # ]
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