I already gave a few basic theories proving .999 and 1 are the same number, but he won't listen to any of them. Does anyone have a good solid one?
If 1 = 1, then .999... =/= 1 for if .999... = 1, then 1 =/= 1. If 1=/=1, .999... = 1 however 1=/=1 , so .999...=.999... and not 1.
Damn the paradox!
Edit, my paradox is confusing me, therefore I will right it out in words:
If one is equal to one, then .999 ad infinitum is not equal to one (reason: paradoxical individuality) for if .999 infinite were equal to one, then 1 would not equal one. In this case, .999~ can equal one since one itself may not, however since one is not equivalent to itself, .999~ is equal to itself and not one and vice-versa.
Paradoxical Individuality: A =/= B, for if A=B...B is actually A *or a division of the whole and B is only a misrepresentation of A.
a = 0.999...
10a = 9.999...
10a - a = 9
9a = 9
a = 1
--------------------------------------
a=.999...
a= (in other words ) infinite (~)
10~=~
10~ - ~ = undefined
(the proof should be denounced at this step, shouldn't it?)
I'm not against .999... = 1
I just need to know.
2006-10-29 08:49:55 · 9 answers · asked by AnnaDuff 1 in Science & Mathematics ➔ Mathematics
I believe that .99999999....... (ad infitum) is indeed equal to 1.
I suppose it could boil down to a philosophical question, depending on your teacher, but my professors at UC Berkeley would say they were equal.
Look at 1/3 * 3 = 1
Now rewrite as 0.333333... (ad infinitum) * 3 = 1
So 0.9999999... (ad infinitum) = 1
~ ♥ ~
2006-10-29 08:55:15 · answer #1 · answered by I ♥ AUG 6 · 1⤊ 0⤋
Why does this rather silly argument come up every day or two?
0.999... and 1 are two different notations for EXACTLY the same number, in the same way as 9/4 and 2.25 and "2 1/4" all denote the same number. If you have an apparent proof that they are different, it is only because you are interpreting 0.999... differently in two or more places in your proof.
2006-10-29 10:45:21 · answer #2 · answered by Anonymous · 1⤊ 1⤋
.999... does =1. Some numbers have more than one decimal representation (we did the proof last year in real analysis). This question is in yahoo answers at least once a week, so you can find many other answers via yahoo answers search.
2006-10-29 09:06:55 · answer #3 · answered by raz 5 · 2⤊ 0⤋
all your paradox crap is right- in itself... it makes perfect sense when read by itself. True
i hate to disagree, but .99999999999999999999999999999
is still not EQUAL to 1.
in a clothing store, a shirt that costs 14.99 is 15 dollars.
in gas prices, a gallon for 2.09999999 is said to be 2.10.
even in regular life... something that is ?.99999999 anything is, for sake of time and reasonability- the next 1 up.
in a laboratory, 12.999 is 12.999... not 13. see?
it all depends on where you are.
hope i could help
-Silence Dogood
ok... hold up. "brad" is right, you get closer at every 9- however never "1"
AND "I LOVE AUG" is right- 1/3x3=1...
however, 1/3 CANNOT be correctly written out as a decimal number. we SAY .33 because that's as close as you're gonna get with decimals
examples: 1/3 of a pie... three pieces that exact size would equall one pie.
.33 of 1 is equall to 33%... 33% x3 is equall to .99, or 99%... NOT a full 100%
see, 1/3 can be multiplied by 3 to get 1, but 1/3 is NOT a number... it is a fraction that can never be written out correctly with decimals
so once again- if you're talking numbers, sure, i wouldn't argue against you, but in the weight of an atom it's not 1 yet.
2006-10-29 09:00:22 · answer #4 · answered by Silence Dogood 2 · 3⤊ 4⤋
Consider this, 2/9 = .22222222 repeating, 3/9 = .3333333 repeating, and 9/9 going by this trend = .999999999 repeating but as we all know a number divided by itself is 1. So I have just shown that 9/9 equals .999999 repeating, and that it also equals 1.
2006-10-29 09:08:36 · answer #5 · answered by Nick G 2 · 0⤊ 1⤋
The formula for the sum of an infinite geometric series is:
q+q^2+q^3+q^4+... = q/(1-q).
Thus, 0.999... = 9*0.1 + 9*0.01 + 9*0.001 + 9*0.0001 + ... = 9*(0.1+0.01+0.001+0.0001+...) = 9*0.1/(1-0.1) = 0.9/0.9 = 1.
2006-10-29 09:20:50 · answer #6 · answered by ted 3 · 1⤊ 1⤋
brad is wrong.
.99999 repeat is equal to one. to whit:
.999rep/3= .3333rep
.3333rep= 1/3
1/3 X 3 = 1
therefore .999rep = 1
2006-10-29 08:58:33 · answer #7 · answered by Cecil 4 · 4⤊ 2⤋
0.999=1 to one significant figure.or if expressing to one decimal place it is also 1.
consider decimal places and significant figures to answer this.
2006-10-29 09:02:32 · answer #8 · answered by Tony B 2 · 0⤊ 3⤋
0.99999......... =/= 1
it does not equal 1 and never will equal 1. Sorry
You're close, very close, getting closer with every 9 you add. But you will never get to 1.
2006-10-29 08:53:16 · answer #9 · answered by Br@d 2 · 3⤊ 5⤋