Does 0.999... equal 1?

calculus says

 

THIS IS WHAT SOME PEOPLE ARE SAYING:
Some people on this thread are giving really bad examples. .333... on to infinity does not equal 1/3. It is the closest representation that we can get on a calculator. If you have .999... to infinity, then 1 - .999...(to infinity) equals 0.000...(to infinity) ... 0001. Therefore there would always be a tiny piece left is what these people are saying.
THIS IS HOW IT IS:
That is technically not mathematically true. This is because when in math some one says .999 to infinity it does not mean that you take that number and add 9s on to it over and over. It means that all the nines are already there. All infinity 9s already exist. If all those nines were to exist, which they can't, which is why it is more theoretical type stuff, then the number would be 1. Since most human minds cannot get this concept into their heads and imagine it. They go with the arguments stated above. Off-topic: its like thinking about death (assuming that there is not god, after-life, etc., etc.) Almost no human mind can actually comprehend not existing. Think about it. If you didn't exist at all after life. Yea, its hard to think about n brings many tough questions. The same basic hard to understand idea applies to this situation which is why you don't really learn about this until calculus and beyond. This is also why they teach you in younger grades just to accept the fact that .333... to infinity equals 1/3 because they don't want to try and teach you thick-skulled people (no offense )

 

And, some fractions can not be properly converted into decimals, thus considering the infinite number.

 

Lol, if you had actually been at Sythe for anywhere near a little while now, you would know it used to be highly debated here.

ON TOPIC:

.99(repeated) ! = 1

 

Ha, the chicken of course. (who else remembers the joke? 'chicken in bed smoking' hahahahaha)

 

Thanks. Very nice.

Why doesn't ?

.333... (ad infinitum) is not an approximation. This is not a rounded value that "we get on a calculator." This value exists at the same point on the number line as 1/3 (aka = )

 

Infinity is not an actual place on the number line, you know.

 

This has gotten pathetic, honestly people.

I don't care what math equations you have to say it is one, trust me, I've done them in classes at much higher levels than you probably have.

Math DOES HAVE FLAWS. It is NOT perfect.

.333... DOES NOT EQUAL 1/3.

FRACTIONS and DECIMALS, ARE DIFFERENT, yet some of you keep thinking they are identical.

.333... does not equal 1/3
.666... does not equal 2/3
.999... does not equal 3/3

I really don't know how much simpler I can explain this in.

Decimals are in powers of 10, it is impossible to divide 3 into 10 and get 3 equal parts in decimal form. Show me that, and I'll never post on this thread again, until then. .999... DOES NOT EQUAL 1.

 

Okay. Let's move out of base ten mathematics. It was true then, and it's true now. They're the same.

 

[sarcasm]Out of the thousands of mathematicians that have concluded that .9(repeated)=1 you have found the real answer. I thank you for that, a true addition to mathematics![/sarcasm]

 

No, but 1/3 is >_>

...

Wow.

Well, for one thing, this image, comes from MathWorld, one of the internet's most extensive math resources. It would seem very odd for the entire math community to be wrong on this matter. Secondly, I have taken calculus in a college setting. So, I doubt the math required for you to explain this is too far over my head. I would be glad to hear it. As the matter of fact, I had a brief discussion about this with one of the calculus professors (he agreed with me).

I don't mean to be rude, but what is wrong with this? This is simple algebra. It doesn't take amazing math skills.

x = .333...
10x = 3.333...
10x-x = 3.333... - .333...
9x = 3
x = 1/3

 

graph it and you will see that you are incorrect. there will be no intercept

 

no. are we forgetting that the 0.001 still counts.

 

What exactly are we graphing o_0?

1/3, .333(repeating), etc are all constants.

 

Take the graph of (x^4)/((x-1)^2). You can see that for x=1, there is a hole, but for any other value of x, no matter how close it gets to 1, there is no hole.

 

if you round

 

then 9.999999999......=10 ?? and 99.9999999....=100 ??
and 999.9999999.....=1000 ???
i dont think so

 

-.- And that was some pointless shit.


Well, 1/3 does not equal to 0.333333333... exactly, as everybody says, it can NOT be converted into decimals properly, thus having to use infinity.

No matter what, 0.9999999... does not reach 1.

 

That is where limit mathmatics takes over and can tell you what should be in an undefined spot. In the case of (x^4)/((x-1)^2) as x approaches 1, f(x) approaches oo.





Limit mathmatics can also tell you the exact value of infinite sums.

In the case of the infinite sum .9 + .09 + .009 + .0009...... which is defined as the sum() of 9*10^-k() starting at 1()and going to n and becuase the decimal places go for infinity n approaches infinity() so:
.999... =


and that equals 1

 

This doesn't really relate to the issue at hand >_>

There is no "hole" in the number line.

1/3 and .333... are constants. They don't "get any closer" to a certain value. They are just like any other real numbers.

Just because the digits in .333... repeat, this does not mean that this number is exempt from normal mathematical principles.

I still have not seen a refutation of the algebra...

Here, I'll do it for another number:

x = 2
10x = 20
10x-x = 20 - 2
9x = 18
x = 2

Does anyone disagree with this? There really is no difference.

EDIT: Nice job with the limits, fatass1.