Who else agrees with me that .999... does NOT equal 1?

Answer 1

Depends on what you mean by 0.999.... Generally speaking the three dots ... indicate that the 9's continue forever. In that case you would have to agree that whatever number 0.999... does represent is within 10^{-n} of 1 for every integer n. This is to say that 0.999... is arbitrarily close to 1. Whether or not you think this implies that 0.999... equals 1 is a matter of personal taste- although much of mathematics is based on the assumption that this does in fact imply 0.999... = 1 (in particular standard calculus is).

There are mathematicians who study so called non-standard analysis in which they reject the above assumption and work with systems of numbers in which 0.999... does not equal 1.

Answer 2

no i disagree that if you said .9999 equal 1 that is not equal 1
if .999 repeat , that is equal 1
i have 3 ways to prove .999 repeat = 1 but i forgot 1 way

u know 1/3 = .33333 repeat , right?
time 3 both sides
(1/3)*3 = .3333 repeat *3
1= .999999 repeat (approve)


other ways can use series to figure out
.999 repeat = .9 +.09+ .009 +.0009 ......... so on., right
that is geometric serie i dont know you have ever heard that before

sum for this serie will be = a1/(1-r)

a1 is the first term, r = second term divide first term , or third term/ second so on.........
a1= .9 , r = .09/.9 = .1
sum .999 repeat = .9/(1-.1) = .9/.9 = 1( approve)

if in mathematic or engineering that is true statement
.999 repeat is equal 1

Answer 3

.999(repeated ad infinitum) = 1 means that the limit of
(9/10 + 9/(10)^2 + 9/(10)^3 + ... is equal to 1. "Limits" either do not exist or are EQUAL TO some number, but they are NEVER "almost" or "not quite" or any any of the other nonsense many of you are spouting.

Consult any standard calculus text for information about limits.

Answer 4

To suggest that a number full of nines is equal to one is, indeed, pretty confusing. But since the real number system can be construed as the set of limits of Cauchy sequences of rational numbers, then 1 is certainly equal to .999..., since you can get arbitrarily close to 1 by going far enough out in the decimal. (Try it if you don't believe me!) In other words, the sequences {.9, .99, .999, .9999, .99999, ...} and {1,1,1,1,1,...} both have the same limit: 1.

(If you're not familiar with Cauchy sequences, then perhaps you'll need a little bit more math before you can fully digest this.)

Answer 5

1/3=.333...
2/3=.666...
3/3=1/3+2/3=.333...+.666...=.999...
But 3/3=1. Hence .999...=1.

I would agree with you if you were right.

Answer 6

Math is not a matter of opinion. If you're working with real numbers, then 0.999... is equal to one. Equal as in identical, the same thing. Not "very close", "tends towards" or any such nonsense.

Answer 7

Depends on the context.. If you round .999 to the nearest whole number it is 1.

Answer 8

Well technically it does not equal one... I don't see how anyone can say that it does equal one, because it does not.
Of course in the day-to-day world, .999 is much easier spoken of as equaling one.

Answer 9

Are you talking about 0.999 or 0.9-repeating? It looks like the latter, but anyway, it isn't a matter of opinion. 0.999 is clearly different from 1. 0.9-repeating is equal to 1, even though this truth is less obvious. It can be proven.

10 * 0.999... = 9.999...
9 * 0.999... = (10 - 1) * 0.999... = 9.999... - 0.999... = 9
0.999... = 9/9 = 1

Answer 10

depends on the number of significant digits you are using. For example if you're digital weight scale at home measures 3.79 pounds but it can only report whole pounds it will display 4 pounds (not 4.0, which means something different).