## Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-) |

# Am I wrong?

### #1

Posted 08 January 2012 - 02:47 PM

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?

### #2

Posted 08 January 2012 - 03:24 PM

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.**

### #3

Posted 08 January 2012 - 03:31 PM

### #4

Posted 08 January 2012 - 03:31 PM

### #5

Posted 08 January 2012 - 04:11 PM

0.333... = 1/3

1/3 + 1/3 + 1/3 = 1

### #6

Posted 08 January 2012 - 05:27 PM

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.

### #7

Posted 08 January 2012 - 06:30 PM

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.

### #8

Posted 08 January 2012 - 09:17 PM

### #9

Posted 08 January 2012 - 09:59 PM

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?

### #10

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.

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users