Question

Does 0.999...=1?

Answer 1

.9999........ is not a number

Answer 2

have you taken calculus?

Answer 3

http://www.math.com/school/subject2/lessons/S2U2L1DP.html

Answer 4

scroll down to number 4, its actaully an easy proof.

Answer 5

you will enjoy calculus:)

Answer 6

Here is an algebraic proof of it:
10x = 9.999999...
with x = 0.99999...
10x - x = 9.99999... - 0.999999...
9x = 9
Thus, x = 1

Answer 7

This question was asked because I was trying to exaplin that inbetween any two numbers is another number, he then said what about .9999999.... and 1, i then tried to explain to him that .99999999.. was not a finite number, then we had this question posted:)

Answer 8

there is no amount of 9's that you can write after .9 that will make it equal to 1, but the limit as the amount of 9's goes to infinity is said to equal 1

Answer 9

wait... doesn't
0.9999... = 9/10 + 9/100 + 9/1000 + ....

an infinite bounded series?

Answer 10

The number "0.9999..." can be "expanded" as:

0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...

Answer 11

lol, read this. then you will see the point of the question
http://openstudy.com/study#/updates/50ab1ceee4b06b5e49334d38

Answer 12

So the formula proves that 0.9999... = 1.

Answer 13

@skullpatrol ok

Answer 14

but .99999...is not a number is the point of this topic

Answer 15

0.999999..... is a no. we have tp prove that it is equal to 1

Answer 16

*to

Answer 17

its a number if you think about convergence, but you can never write 1 in the form .999999999999, read the last question and you will see the point im trying to make

Answer 18

its not a finite number.... it can be looked at as a sequence....at infinity then its a number.

I told him that between any two numbers is another number, he then said what about .99999999999..... and 1, this is what followed.

Answer 19

Its an extended real number in the since that infinity is an extended real number....

Answer 20

"But", some say, "there will always be a difference between 0.9999... and 1." Well, sort of. Yes, at any given stop, at any given stage of the expansion, for any given finite number of 9s, there will be a difference between 0.999...9 and 1. That is, if you do the subtraction, 1 – 0.999...9 will not equal zero. But the point of the "dot, dot, dot" is that there is no end; 0.9999... is inifinte. There is no "last" digit. So the "there's always a difference" argument betrays a lack of understanding of the infinite. (That's not a "criticism", per se; infinity is a messy topic.)

Answer 21

right and i dont think he has had calculus...

Answer 22

this started with density of rational/irational and archimedes principle on the real line

Answer 23

the point is, that there is an infinite amount of numbers between any two numbers a,b where a != b

Answer 24

hahhaha.. we are just fighting you and me are absolutely right...it's a skull problem..right??

Answer 25

right?? @zzr0ck3r

Answer 26

This one might make him want to quit math
The infinite amount of numbers between 0,1 is larger than the infinite amount of numbers between 0 and infinity.:)

Answer 27

right:)

Answer 28

:)

Answer 29

0.9999 is approximately equal to 1 but it is not exactly equal..

\[0.999 \approx 1 \qquad \qquad (0.999 \ne 1)\]

Answer 30

got it @skullpatrol

Answer 31

this question...lol

Answer 32

http://www.math.hmc.edu/funfacts/ffiles/10012.5.shtml

Answer 33

can you provide a proof of this ...
"This one might make him want to quit math The infinite amount of numbers between 0,1 is larger than the infinite amount of numbers between 0 and infinity.:)"

Answer 34

no, my analysis teacher said it two days ago. she said the elemnts between 0 and 1 have more mappings than 0-infinity

Answer 35

your teacher is either wrong or you have misquoted her

Answer 36

the real numbers between 0 and 1 is the same size as the real numbers from 0 to infinity

Answer 37

\[1 - 0.999\cdots = 0.000\cdots = 0\]