Question

Find a number between 0.999... and 1.

Answer 1

lim x->1-

Answer 2

0.9999

Answer 3

Is this a trick question? :/

Answer 4

-0.999

Answer 5

It is a "make you think" question.

Answer 6

Does there exist an x such that $$\Huge0.999...<x<1$$

Answer 7

x must be larger than 0.999... AND smaller than 1

Answer 8

there are infinite number between the open interval \((0.999, 1)\)

Answer 9

https://upload.wikimedia.org/wikipedia/commons/thumb/e/e5/999_Perspective_Vector.svg/300px-999_Perspective_Vector.svg.png

Answer 10

\[0.999\ldots = \sum\limits_{n=1}^{\infty} \dfrac{9}{10^n} = 1\]

Answer 11

question is same as finding a number between 1 and 1

Answer 12

so its empty set

Answer 13

If you cannot find a number between 0.999... and 1,

then they are the same number.

Answer 14

empty set is a correct answer

Answer 15

The objective is to write down the decimal number which is larger than 0.999... but less than 1.

Answer 16

@skullpatrol

People have been debated that for years now. Whether or not 0.999 equals 1. Some say it does, while others say it does not.

Answer 17

Try to "think about it" @Night-Watcher How can you make 0.999... any bigger?

Answer 18

0.999 is not 1

0.999... is exactly same as 1 however

Answer 19

By adding other 9's at the end.

Answer 20

But there are infinitely many 9s on the end...it is endLESS

Answer 21

Just like 1/3 = 0.333...

Answer 22

but see 2/3 = 0.666...

Answer 23

1/3 + 2/3 = ?

Answer 24

1

Answer 25

0.333... + 0.666... = ?

Answer 26

0.999....

Answer 27

there are many tricks

\(\large \begin{align} \color{black}{x=0.99999999......\hspace{.33em}\\~\\
10x=9.9999999......\hspace{.33em}\\~\\
10x=9+0.9999999......\hspace{.33em}\\~\\
10x=9+x\hspace{.33em}\\~\\
9x=9\hspace{.33em}\\~\\
x=1
}\end{align}\)

Answer 28

It's equal to 1, so there can't be a number between. 0.999 as a decimal equals 9/9 which equals 1!

Answer 29

0.999000 can be written as the fraction 1

Answer 30

0.999000 it is different from 0.99999........

Answer 31

10x = 9.99
- x = 0.999
----------
9x = 8.991.

Answer 32

to solve 9x=9 we divide both sides of it by 9, and we'll get that x=9/9.

Answer 33

Then 9/9 reduced is 1

Answer 34

@Night-Watcher you're missing the idea of "infinitely many" nines...

Answer 35

https://upload.wikimedia.org/wikipedia/commons/thumb/e/e5/999_Perspective_Vector.svg/300px-999_Perspective_Vector.svg.png

Answer 36

*sigh* What i'm going to be doing after finding out the answer.

http://wac.450f.edgecastcdn.net/80450F/thefw.com/files/2013/05/SPoiler.gif

Answer 37

If I want to increase the size of a decimal number I must increase one of its digits to the next larger one. For example, 0.752 < 0.762 because I increased 5 to 6, right?

Answer 38

Or 0.333... < 0.343... because I increased 3 to 4.

Answer 39

Now with 0.999... if I increase any of the 9s by one I will get a 0,

For example 0.999... + 0.01 = 1.009...

Answer 40

But look that is larger than 1.

Answer 41

0.999 + 0.001= 1

Answer 42

And 0.999 + 0.0001= 0.9991

Answer 43

So would that number be between the two?

Answer 44

Nope. You need to add 0.999... + 0.0001

Answer 45

There is no number 0.0001 that you can add to 0.999... that will not make it larger than 1

Answer 46

00.9999999...
+0.00001
-----------
1.00000999... > 1

Answer 47

Any tiny, tiny number you add to 0.999... will make it greater than 1,

so that must mean there is no number "between" and that can only be if they are the same

Answer 48

Touché.

Answer 49

If we have 0.000000000000................................................1 at the last, then??

Answer 50

the empty set makes a good answer like @mathmath333 said

Answer 51

@eta if you have a "last 1" on the end of your

"0.000000000000................................................1."

Then

0.9999999999999999999999999999999999999999...
+.000000000000................................................1
----------------------------------------------------
1.0000000000000000000000000000000000000999... > 1

Answer 52

At the end means, where 9 will end.. If it is not ending, then add that 1 to that non-ending end. :P

Answer 53

Can there be an end to something that does not end? @eta