They're exactly right. Form a basic calculus perspective, you can think of it as an infinite sum where you keep adding on a 9 at the end. Since the sum converges, you end up with 1. Graphically, there is a asymtpote at 1 when you approach infinity, ergo .9999 repeating [I]is[/I] 1.
The answer is .3∞
3.
Most calculators will round 2/3 to 0.66666666667
[QUOTE=JohnnyMo1;43779757]3/3 [I]is[/I] 0.999 repeating because 0.999 repeating is 1.[/QUOTE]
I do agree that 0.999 repeating is equal to 1. But 3/3 still comes out to 1.
I don't know if any teacher or professor would honestly accept 0.999 repeating as an answer for 3/3.
Wouldn't you be able to argue that any number divided by itself is 0.999 repeating then?
[IMG]http://upload.wikimedia.org/math/4/7/e/47e0d646891053c1f3b41fa8c81b6ebb.png[/IMG]
proof that .999...=1
.33 + .66 = 1 because reasons.
It is a thing called rounding.
[QUOTE=Tmaxx;43780986].33 + .66 = 1 because reasons.[/QUOTE]
0.33 + 0.66 = 0.99
0.333... + 0.666... = 0.999... = 1
This is why infinite decimals aren't used in actual math, they make things way too complicated. The fraction notation is so much better
[QUOTE=Sgt. Khorn;43780870]I do agree that 0.999 repeating is equal to 1. But 3/3 still comes out to 1. [/QUOTE]
Then equality is not transitive, but it is, so you are incorrect. If a = b and b = c, then a = c. 3/3 = 1 and 1 = 0.999..., thus 3/3 = 0.999...
[QUOTE=Sgt. Khorn;43780870]I don't know if any teacher or professor would honestly accept 0.999 repeating as an answer for 3/3. [/QUOTE]
Well it would be kind of silly to write it that way, but technically the answer is the same so there's no reason they shouldn't accept it. Teacher I can understand, but a math professor should recognize that 0.999... = 3/3. They may think you're a little odd, though.
[QUOTE=Sgt. Khorn;43780870]Wouldn't you be able to argue that any number divided by itself is 0.999 repeating then?[/QUOTE]
Yes, because any number divided by itself (zero excluded) is one, and one is 0.999...
[QUOTE=JohnnyMo1;43773226]The one in that video that you mentioned in the post just above is pretty good, the fact that there is always another number between two real numbers. If they can't name the number in between, they must be the same. If they're not convinced of [I]that[/I] fact, the proof of it is maybe a little long for most people, but elementary, requiring nothing more than basic algebra.
My favorite one though is using the geometric series summation formula to add up 0.9 + 0.09 + 0.009... etc. It's pretty easy to convince someone that that has infinitely many terms, or else it's obviously a different number than one but not the "closest" number to one, which many people are convinced 0.999... is. Then you can equate 0.999... = sum from 0 to infinity of (9/10)(1/10)^n, derive the geometric series formula (which is quite elegant and convincing and requires only algebra and taking one limit) and apply it to show that it's just 1.
If they [I]really[/I] have problems, and don't accept that the limit in the proof of the geometric series formula works, then you can do it directly with a limit, showing (or just declaring, as it's pretty intuitive) that the sum of an infinite series (e.g. 0.9 + 0.09 + ...) is the limit of the sequence of its [I]partial[/I] sums, i.e. {0.9, 0.99, 0.999, ...}. If they have misgivings about limits (a lot of people see it as a kind of process, not simply a value), it's not hard to apply the limit definition [I]directly[/I] to the sequence to show that its limit is 1.
[editline]3rd February 2014[/editline]
There are absolutely no mathematicians that disagree with "0.999... = 1," except maybe N. J. Wildberger, but he is a crank.
I don't know that he disagrees, but he disagrees with the foundations of set theory on which all modern mathematics is based and nobody really takes him seriously.
Actually now that I think about it, Wildberger and other radical finitists probably reject the question entirely, since infinite decimals don't have any meaning to them.[/QUOTE]
So essentially it's a Calc II problem. I actually came into this thread to mention that it was calculus II level and you get into sums of series, but then I saw you enter the thread and knew it wouldn't be necessary.
[editline]4th February 2014[/editline]
OP, I did this level math in my first year of uni, what level schooling are you in, and how much math have you done?
Well 0.(9) isn't 1 per se, just the difference between it 0.(9) and 1 will be always infinietly small, It's basically impossible to measure. That's why it's just considered to be the same(or should I say "equal"?).
[QUOTE=BananaMed;43789537]Well 0.(9) isn't 1 per se, just the difference between it 0.(9) and 1 will be always infinietly small, It's basically impossible to measure. That's why it's just considered to be the same(or should I say "equal"?).[/QUOTE]
No, 0.999... is 1 per se. 1 - 0.999... = 0 identically. This is not an issue of rounding or what we can measure.
[QUOTE=WastedJamacan;43785835]OP, I did this level math in my first year of uni, what level schooling are you in, and how much math have you done?[/QUOTE]
9'th grade math as one of the better students only.
But I am afraid that doesn't count anymore, I have forgotten a lot of the stuff I know.
(And my school seemed more interested in geometry, which I was terrible at.)
It still is pretty interesting to read about, and sorry for seeming like an idiot.
[QUOTE=gokiyono;43794965]9'th grade math as one of the better students only.
But I am afraid that doesn't count anymore, I have forgotten a lot of the stuff I know.
(And my school seemed more interested in geometry, which I was terrible at.)
It still is pretty interesting to read about, and sorry for seeming like an idiot.[/QUOTE]
It's alright, IIRC 9th grade level is Algebra, right? You've got a long way to go before you get into sums of series (like, 3 years of HS level math and 2 semesters of college level math)
[QUOTE=WastedJamacan;43800941]It's alright, IIRC 9th grade level is Algebra, right? You've got a long way to go before you get into sums of series (like, 3 years of HS level math and 2 semesters of college level math)[/QUOTE]
We had algebra, yeah.
But there were a lot more focus on geometry and trigonometry at my school.
Sorry, you need to Log In to post a reply to this thread.