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# Am I wrong?

12 replies to this topic

### #1 wolfgang

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Posted 08 January 2012 - 02:47 PM

Let X= 0.9999.............
then 10X=9.99999..........
10X- X = 9.99999......... - 0.999999.......
9X = 9
that means:
X=1
so
1= 0.999999........
the same is in case of:
1/3+1/3+1/3 =3/3 = 1
but, 1/3 = 0.33333.........
so
0.333333......+0.33333.....+0.33333.......= 0.999999.......
which is < 1
Am I wrong?
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### #2 SMV

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Posted 08 January 2012 - 03:24 PM

Interesting puzzle....

I think that though 0.9999... stretches to infinity, it is not right to say that 9.999.... - 0.999.... is equal to 9.
It may be very close, but not equal to 9.

Edited by SMV, 08 January 2012 - 03:27 PM.

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### #3 Arjit Saraswat

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Posted 08 January 2012 - 03:31 PM

interesting...
Spoiler for i think

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### #4 thoughtfulfellow

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Posted 08 January 2012 - 03:31 PM

Spoiler for well

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### #5 witzar

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Posted 08 January 2012 - 04:11 PM

0.999... = 1
0.333... = 1/3
1/3 + 1/3 + 1/3 = 1
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### #6 donjar

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Posted 08 January 2012 - 05:27 PM

I agree with the comments already posted. The infinite decimal 0-99999.... is equal to 1.
However, while on the subject of fractions, figure this out:
10/10=1; 9/9-=1; 8/8 =1 .......1/1=1, so 0/0 = 1
Now 0/10 =0; 0/9=0; ......0/1=0 and so 0/0=0 !
Further, 10/0 = infinity; 9/0 = infinity, ... 1/0 = infinity, so 0/0 = infinity !
Show the flaw in the logic.
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### #7 magician

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Posted 08 January 2012 - 06:30 PM

.9999999999... is equal to 1.
consider the geometric series 9*(1/10)^n from n=1 to n=infinity
the series can be written .9+.09+.009+.0009+.00009+.000009...
the sum of the series is 9*(1/(1-1/10)-1)=9*1/9=1

As for donjar, x/0 is not infinity. It is undefined unless it is taken as a limit, but I will proceed under the assumption that that is what you mean. regardless, those three functions are not continuous at x=0. In fact, the value of 0/0, strange as it may sound, is dependent on context.
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### #8 mewminator

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Posted 08 January 2012 - 09:17 PM

the number of 9's after the decimal point should decrease by 1, I know infinity-1 is still infinity, but in this case it would be a different value,9.99999 x 10 would be 99.9999,so the 9's after the decimal should decrease, but stay infinity, though I don't know how to achieve that
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### #9 SeaCalMaster

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Posted 08 January 2012 - 09:59 PM

For those of you who aren't convinced that 0.999... = 1, here's something to think about.

We all know that pi is irrational. However, we've come up with a numerical representation of pi: 3.1415926.... My question to you: what do we mean by that sequence of digits? Can you define it in terms of rational numbers? Then, how would that apply to 0.9999?
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### #10 fwang

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Posted 08 January 2012 - 11:28 PM

I agree with the comments already posted. The infinite decimal 0-99999.... is equal to 1.
However, while on the subject of fractions, figure this out:
10/10=1; 9/9-=1; 8/8 =1 .......1/1=1, so 0/0 = 1
Now 0/10 =0; 0/9=0; ......0/1=0 and so 0/0=0 !
Further, 10/0 = infinity; 9/0 = infinity, ... 1/0 = infinity, so 0/0 = infinity !
Show the flaw in the logic.

Division by zero does not equal infinity or zero. Dividing by zero causes the line to diverge. If you take the limit* of 1/x as x approaches 0 from the positive side, it goes towards positive infinity. If you take the limit of 1/x as x approaches 0 from the negative side, it goes towards negative infinity.

A few problems that will illustrate this point:

1/1 = 1; 1/-1 = -1

1/.1 = 10; 1/-.5 = -10

1/.01 = 100; 1/-.01 = -100

1/.000001 = 1000000; 1/-.000001 = -1000000

etc.

*Taking limits is something you will learn in Calculus 1 if you aren't already aware of the concept.
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