Does 0.999~ = 1? [oldskool debate]

Nvm it does equal 1.

 

What's your source for this? Some of you say this can't be debated, I think it's because you guys don't know how to debate :O!

@imagine I haven't mixed up signs in the OP, 10x-x=9 when x=0.9~

 

You have x - 10x @ mohtasa. it should be 10x - x,

 

Interestingly enough, no matter what numerical system is used, including hexadecimal and binary, this fraction always results in a recurring number (EG 0.FFFFF or 0.010101)

 

Ohlul


@ Sweet Vengence, you need to post your reasoning, SFA doesn't benefit from "lol i disagree kbye"

 

According to any proof you do, it definitely does. However, I honestly don't think it [truly] does once written down.

Personally, the problem lies in converting decimals to fractions. It converts an exact value of your fraction to a NON-exact decimal answer. The repeating sign implies and infinite number of the repeated sequence, but it is never truly an exact value of one UNLESS you reach the end of that infinite sequence [which you never will]. It might be so close to 0 that it's basically incomprehensible, but from what we can physically do, the values aren't equal and will never be equal.

It's hard for me to explain. The values are obviously equal IN PROOF, but when written, it's impossible for anyone to reach the end of that repeating sequence to back up the validity of the proof.

 

Damn. I've just been mind blown. This is a bit much for a Geometry 1 Sophomore but hell. I can't decide what's right an what's wrong. If you put it into fractions, Yes it does work, I think?.. And then vice versa with decimals?.. Ehh, my brain hurts..

 

.9999999999999 does not equal 1. At least, not in high-level physics. Especially quantum physics and general relativity.

 

Numbers are fake. They are a manifestation of our minds to describe something, similar to words. Just because we say "red" doesn't mean something is red. what is red? Languages and math are very similar. Math is universal...at least for our planet though. .999~ does not = 1. But what .999~ repeating represents, does in fact equal what 1 represents.

 

Okay those proofs are great and all, but explain why they're true and why an infinite number of 9's after 0. is equal to one.

 

He wasn't rounding, the tildes there are to imply that the numbers are recurring.
e: disregard that you edited your post

???
Because of the proofs he posted?

 

Numbers are fake? Oh my

That fact that we rationalize the properties of the world around us doesn't make what we call "red" fake, same with numbers. What we call red is something real-- and everything similar to that something real, we call red. And how does that make it a manifestation of the mind? By the way, "manifestation of the mind" means "the action of showing the mind in such a way" (i.e. a computer chipset is a manifestation of the brain), I don't think that's what you're trying to say, but be care with your vocabulary. A more proper phrase to express what I think you're trying to say is "a figment of our minds/imaginations". Given that phrase, you'd be saying "we see something, imagine it somehow connected to the word 'red', and suddenly it's red, but that doesn't mean it's really what we think it is".......... But I digress.

Anyway, language and math are two drastically different concepts. Again, I THINK I understand what you're trying to say, and that is that both languages and mathematical computations are abstract at best... but mathematics is not abstract, it's absolute (although some of our hypothesis may not be 100% accurate). How we express it with numbers and symbols may be an abstraction, but what they represent are real.


To what you said before you edited: I did not round, ~ is a mathematical representation for infinitely recurring. Divide 1 by 3, and any calculator will give you a rounded number because the three's do in fact go on forever.

 

The limit as 3/3 [1/3 being .333333333 forever, multipled by 3] approaches infinity is 1.

 

It's regardless of what you're using. if the 9's are recurring, then it does equal one.

The number you posted does not, but that's because it does not go on forever.

Another proof:

You can always think of a number between one number and its next. (If they are distinct numbers, just add one more decimal place and put .5 there).

Think of a number between .999~ and 1. That's right. You can't. Because they are the same number.

I'd also like to point out that .999~ is just another way to represent one. Just like we can represent 1/2 as 2/4, they are the same number.

 

But it's actually one when the end of that infinite sequence is reached. But it won't ever reach that end because infinity's simply a concept, not a number.

I see why it should equal 1, and I'm starting to believe it does, but the repeating sequence will never actually reach one. It will never become one until that infinite number of 9's is reached. But that infinite number won't ever be reached, so it really shouldn't be equal to one.

 

You can assume that there are an infinite number, you don't have to keep adding on 9's.

 

But if they're equal, at what point does .99 repeating equal one?
(what point in the sequence can you conclude it is finally equal to 1)

 

I am not going to lie, you just blew my mind. I'm on your side lol

 

You can only assume it's one when you find out it repeats forever... it doesn't matter how many digits long it is, unless it goes on forever, and you have definite proof, you can't declare it's one.

 

There is very little debate to be had. Your first proof (a slightly longer, more formal version) is accepted as definitive by almost the entire math community. It's about as true as 1=1 at this point.

Also, if this is invalid then limits are invalid (based on infinitely close numbers being equal) and therefore most of calculus is invalid, along with much of the physics derived from calculus for which experiments have always complimented the numbers.

Edit: Everyone on Wikipedia also seems to agree: http://en.wikipedia.org/wiki/0.999...

Second Edit: You messed up the first proof a bit (you get x=-1 because you reversed what should be subtracted)

As Jimmy said, there is no debate and the thread should be closed, but you are educating people on mathmatical topics so I guess it's good...