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Math Forum » Discussions » Math Topics » alt.math.undergrad.independent

Topic: how does .9999999=1???
Replies: 19   Last Post: Jan 1, 2011 2:43 AM

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ben

Posts: 1
Registered: 12/10/04
how does .9999999=1???
Posted: Jun 4, 2003 5:43 AM
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for .88888888 to infinity, let x=.88888888 then 10x=8.8888888888, so
10x-x=9x=8 and x=8/9 which makes sense because .888888 to inf is
rational as a repeating pattern, not irrational
ALSO x=.7777777 to infinity, then 10x=7.7777777 to infinity so 9x=7
then x=7/9
BUT if x=.99999999999 to infinty and 10x=9.9999999999 then 9x=9/9=1
which does not equal .9999999999 to inf, this implies that the endless
decimal .9999999999999 etc is irrational since it cannot apparently be
expressed as a quotient of two integers a/b.
whatsup with this????

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