wolfgang Posted January 8, 2012 Report Share Posted January 8, 2012 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? Quote Link to comment Share on other sites More sharing options...

0 Guest Posted January 8, 2012 Report Share Posted January 8, 2012 (edited) 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 January 8, 2012 by SMV Quote Link to comment Share on other sites More sharing options...

0 Guest Posted January 8, 2012 Report Share Posted January 8, 2012 interesting...i think the statement is correct .... as the diff. b/w 1 & 0.999..... is 0.000....(infinite 0's)1 which is actually nothing.. so there's no difference b/w 1 & 0.999.... think about it this way... 1/9 = 0.111........ 0.111..... * 9 = 0.999....... but 1/9 * 9 = 1 therefore...... 0.999.... & 1 are same Quote Link to comment Share on other sites More sharing options...

0 Guest Posted January 8, 2012 Report Share Posted January 8, 2012 As strange as it looks, you are definitely correct in your first example. The repeating decimal, 0.99999.... does in fact = 1. Thiis does mean you are wrong when you say 0.9999999... <1. Your first method is the technique for converting a repeating decimal into a fraction. If you use the same teqnique for 0.3333..., you'r answer will be 1/3. Likewise for 0.666666... to be 2/3. Quote Link to comment Share on other sites More sharing options...

0 witzar Posted January 8, 2012 Report Share Posted January 8, 2012 0.999... = 1 0.333... = 1/3 1/3 + 1/3 + 1/3 = 1 Quote Link to comment Share on other sites More sharing options...

0 Guest Posted January 8, 2012 Report Share Posted January 8, 2012 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. Quote Link to comment Share on other sites More sharing options...

0 Guest Posted January 8, 2012 Report Share Posted January 8, 2012 .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. Quote Link to comment Share on other sites More sharing options...

0 mewminator Posted January 8, 2012 Report Share Posted January 8, 2012 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 Quote Link to comment Share on other sites More sharing options...

0 Guest Posted January 8, 2012 Report Share Posted January 8, 2012 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? Quote Link to comment Share on other sites More sharing options...

0 Guest Posted January 8, 2012 Report Share Posted January 8, 2012 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. Quote Link to comment Share on other sites More sharing options...

0 Guest Posted January 8, 2012 Report Share Posted January 8, 2012 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. It depends on the system you're using; however, most of the time, division by 0 is undefined. Division by a number is equivalent to multiplication by that number's multiplicative inverse, and 0 does not have a multiplicative inverse in any ring. If your domain is, say, the Riemann sphere, division by zero is meaningful, but one assumes that we're using the reals here. Quote Link to comment Share on other sites More sharing options...

0 Guest Posted January 9, 2012 Report Share Posted January 9, 2012 Interesting! yes you are quite right, but there are no difference between 1 and .999999..........(to infinite). But you mention that, 0.999999.........<1, it's incurrect. That way 1/3=0.33333333...... and, 1/3+1/3+1/3=0.3333....+0.3333....+0.3333....=1 (or 0.99999.......) Quote Link to comment Share on other sites More sharing options...

0 bhramarraj Posted January 20, 2012 Report Share Posted January 20, 2012 Since many of the friends have not used spoiler so i am also not using it. I think unless we do not ascertain a fixed value to an unknown quantity, say X, we can not apply mathematics to this quantity with respect to other quantities. For Example X could be treated as 0.999 and then 10X = 9.99, So 10X - X = 9.99 - 0.999 = 8.991 or 9X = 8.991; Now we may see that X can not be equal to 1. Without ascertaining a fixed value to a certain parameter we may fall into infinity.....!!!!!! Am I right...? Quote Link to comment Share on other sites More sharing options...

## Question

## wolfgang

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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