Jump to content


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 :-)
Guest Message by DevFuse
 

Photo
- - - - -

Am I wrong?


  • Please log in to reply
12 replies to this topic

#1 wolfgang

wolfgang

    Senior Member

  • Members
  • PipPipPipPip
  • 781 posts
  • Gender:Male

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?
  • 0

#2 SMV

SMV

    Advanced Member

  • Members
  • PipPipPip
  • 140 posts

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.

  • 0

#3 Arjit Saraswat

Arjit Saraswat

    Junior Member

  • Members
  • PipPip
  • 80 posts

Posted 08 January 2012 - 03:31 PM

interesting...
Spoiler for i think

  • 0

#4 thoughtfulfellow

thoughtfulfellow

    Advanced Member

  • Members
  • PipPipPip
  • 218 posts

Posted 08 January 2012 - 03:31 PM

Spoiler for well

  • 0

#5 witzar

witzar

    Advanced Member

  • Members
  • PipPipPip
  • 233 posts

Posted 08 January 2012 - 04:11 PM

0.999... = 1
0.333... = 1/3
1/3 + 1/3 + 1/3 = 1
  • 0

#6 donjar

donjar

    Junior Member

  • Members
  • PipPip
  • 97 posts

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.
  • 0

#7 magician

magician

    Advanced Member

  • Members
  • PipPipPip
  • 135 posts

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.
  • 0

#8 mewminator

mewminator

    Advanced Member

  • Members
  • PipPipPip
  • 258 posts
  • Gender:Male

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
  • 0

#9 SeaCalMaster

SeaCalMaster

    Junior Member

  • Members
  • PipPip
  • 27 posts

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?
  • 0

#10 fwang

fwang

    Newbie

  • Members
  • Pip
  • 3 posts

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




0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users