0.999... = 1

anyone can play tricks with algebra.

Let me show you an algebra trick.

X = 0.9999...9
Y = 1.000...0

Y/X = 1
X/Y =/= 1 = 0.9recurring

oh no!!!! the horror!

Y - X =/= 0 = 0.0000...1
∴ Y =/= X

There. Nothing more needs to be done.

the fault in your algebra trick is that it literally proves itself wrong, not right. You just proved that you can't have anything .9recurring, because it's an irrational number that's impossible, whereas 1.0recurring is entirely possible and rational, real etc. 0.9recurring is a fake value people pretend exists because they are enslaved to denary counting system and can't get over the fact that math is not pure logic; it's a limite format of displaying and comprehending it.

0.9recurring is a fake number, a bullshit number. It doesn't even equal itself according to your equation, LOL! Why didn't your answer say M = 0.9recurring? I wonder why.

@RM
You're hopeless.
I'll just leave you with this (it's proving 9.999...=10, but it's the same concept as 0.999...=1):

M = 9.999999... <--- All 9s forever
10M = 99.999999... <--- All 9s forever

10M = 99.999999...
- M = 9.999999...
--------------------------------
9M = 90.0000000... <--- All 0s forever (9 - 9 = 0)

9M/9 = 90.0000000.../9
M = 10.0000000... = 10

Nothing in your infinite series calculations explains how you ever can add infinite number of things, you can't ever reach the last one to add it. It also fails to appreciate that if 0.9r is a possible constant, then so is the difference between it and 1.0r

I already covered how you cannot ever validate 0.9r as anything other than a bullshit value that doesn't even exist unless you validate that the difference between it and 1.0r is as real as it, itself.

you are saying sum of an infinite series, an infite series never can be added together, it never ends to finish the adding.

no thank you, will you look at my solid proofs (plural)? No. Then fuck off with your hypocrisy.

Look at my proof again. Tell me exactly what is wrong with it.

If you can’t do that, then my proof is solid and 0.999...=1

Same to you "PressF4"

@RM
Did you even look at my proof?
If not, then you are willfully ignorant.
If so, then you are downright stupid.

I hope billa comes back, i thought of an epic final argument to seal the case 110%

And this is why debates have limited rounds. We will have to agree to disagree. Good debate. 🍻

The last digit of pi is no less impossible to reach than the last 9 in 0.9recurring.

If you've never come across an infinite series that doesn't happen to be the same over and over again and think in any shape or form the number repeating being the same digit makes it remotely more possible of a value, you're simply too logically blinded to conprehend the truth.

0.9r9 is as ridiculous as the difference between it and 1.0r0, which is 0.0r1

I'm merrily reminded of a debate I had which stemmed from someone bad at math insisting 1-1=2, and claiming anyone (probably calculators as well) who disagrees are trolls:
https://www.debateart.com/debates/803/default-auto-loss-on-forfeit

Btw, I've adopted your notation for this conversation, but you do know XrY is already an existing notation? r=remainder. Just fyi cause it might create confusion in the future. Repition is notated with ... or a bar over the repeating numbers. I know it's a made up convention, but it makes discussing it alot easier when everyone agrees.

I dont know where 0.0r1 even came from. Just to clarify, 0.0r1 means 0.000....1? I have never encountered a repeating number that suddenly stopped repeating. That defies the very definition of a repeating number. This makes no sense.

If its the same numbers repeating over and over again, there is no last number to reach! This also makes no sense! Is that last number in the millionth spot? The billionth? If you claim it must eventually end, where?! You are no longer taking about repeating decimals if the repitition stops.

Your dichotomy is false. It is a number, and you can't reach the end of it. Infinity is not a number, but numbers are infinite. In every direction.

Don't you see?

If you say 0.0r1 never reaches the one, guess what? It never reaches the last of any decimal that's recurring at all.

Just because it's the same digit over and over again doesn't make it any less impossible to reach the final value on the series. Either 0.9r is not a number and can't equal 1, or it is a number and the last 9 is as reachable as the last 1 in the 0.0r1 difference.

Ummm y=1-1 doesnt establish that anything doesnt equal zero. And It it still doesnt explain where 0.0r1 came from to begin with.

Did you mean 0.0r0 with a 1 somewhere at the end of time? Because that is what 1-0.999... would incorrecrly represent. 0.0r1 makes no sense at all anywhere in your math.

At this point i think you should drop the first part of your name.

0.0r1 * 0.0r1 = 0.0r1

pretty simple for someone who is good at math.

Why not just say y = 0 you ask?

answer is because you don't seem to understand that 0 =/= 0.0r1

:)

Also, what was the point of 1-1 = y. Why not just say y = 0.... or just use a zero. The point of a variable is to solve for it.... this is very sloppy math.

Im sorry, your equations do not follow. Problem number 1 is that you are using what your trying to prove in your premises, which leaves you open to circular logic. #2, where did 0.0r1 come from? As far as i can tell x*x = 0*0 = 0. Thats the problem when you use your conclusion in your premise.

Math doesn't lie?

1 - 0.999... = X

1 - 1 = Y

Y * X = 0

X * X = 0.0r1

Y * Y = 0

Y / X = 0

X / Y = cannot divide by zero

Y / Y = cannot divide by zero

X / X = 1

:) I can do this all day, want to stop the algebra mechanics? I will run rings around you, of course math can lie just as much as tell the truth.

If Russia or China went to the UN and said 'hello, after agreeing to lie for a while, we wanted to let you know that this actually is all bullshit and we and NASA lied all along please condemn US along with us' what would happen?

X = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
X = 9/9 = 1

Math doesnt lie.

It isnt just nasa, its a world wide concensus including competing intellectual institutions and enemy nations. Thats 1 heck of a coverup.

Lets leave the flat earth discussion for another day.

Now I laughed, that felt good.

10x method shows the bullshit of 0.9r = 1

9.anything clearly isn't 10.0r LOL

The Earth has never been proven to be round, only assumed to be so as long as you trust NASA and Roscosmos.

All experiments that conclude curvature of the Earth, assumed that the distortion across distance is due to the curvature and not due to a literal maximum of vision existing where a horizon squashes everything into the ground no matter what.

No, they didn't, they came up with it but didn't prove it.

No, it is well known that the greeks had proven the roundness of the earth, and all educated people of Columbus's time, including columbus, knew it was round.

My initial proof did not use 1/3 as a precondition. It involved the x10 method, and no prenotion of an existing equality.

There's no elaboration, no such extension of anything.

They go from telling you it was columbus to telling you that an animated CGI graphics image of a round earth by a government agency that has top level security clearance and due to that is too secret to ever be audited properly, told you it was round.

They go from telling you 1/3 = 0.3r to telling you the same thing multiplied by 3, which was a lie in the first place.

Yes, those do exist in early education. Like how they teach that columbus proved the earth was round... but once you get to college, those simplifications are eliminated. This proof is only really discussed in advanced math classes in college, i dont think convenience is a thing. And even if it was, like the facts about columbus and the round earth, we would see detailed elaborations. The conclusion that it =1 is the most detailed elaboration.

It is not a conspiracy, it is a lie for convenience.

Like i understand questioning certain aspects of history as the details of which can be very political, and many soueces biased.... but math!!!! Why would there be a nation (or actually world wide) conspiracy about the value of 1/3?!? That is absurd.

I did read it, i thought about it, and i came to the conclusion that you dont quite understand the concept of infinity.

Appealing to expert opinion within their field is a valid way to seek knowledge. Appealing to mass opinion is not a valid way to seek knowledge. I do not know you, or your qualifications. I have no way of verifying it. So unless you feel like disclosing personal information (which i am not asking for), i cannot use your expertise as evidence. You can make an argument, but you cannot reference yourself as proof. If i make an argument regarding my field of expertise, medicine, i will still have to cite a source beyond me. Thus self declarations of any kind are taken with a grain of salt. Your intelligence is known only to you and is anecdotal to anyone else.

It is a shame you are taking calm deliberation with arguments and citations as laughing. It appears you are becoming emotional. If you like we can settle this with an agree to disagree, but in my personal opinion, your arguments are unsatisfactory. I am not the only person of this opinion so far. Also, i support education and i find most people who reject it to be predisposed to alot of false knowledge that they declare with absolute confidence. My opinion is open to change, it has changed on this exact topic before. Your declarations of certainty and conspiracy (around education) do not sound like they are open to change.

Do you think typing 'no-one out of the experts agrees with you' makes it true? I am an expert in logical reasoning and mathematics myself but I guess any others who agree with me don't exist or are disqualified yeah?

What makes you being impressed with my self-declared intelligence in any shape or form the means to qualify or disqualify it? You have no superior or inferior objective weight than I do, in terms of your approval of my intelligence mattering vs my own approval of it. If only fools claim to know more than everyone else (it's 'than', not 'then' by the way), then you should not claim to know more than everyone who says that 0.9r doesn't equal 1, or else you're a hypocrite.

I didn't laugh at the concept in this entire chat, if anyone is being sardonic and laughing the other down, it's pressf4respect and yourself. Did you even read what I said is the actual value of 1/3 in decimal numbers? Did you actually read it and think?

If by majority you mean the masses of lay people who never looked into the matter, then yes. But as far as expert opinion in regards to people who actually study and work with numbers, noone agrees with you.

Self declared intelligence in defiance of education does not sound impressive. I am only citing a cliche saying when i state that only fools claim to know more then everyone else.

When this concept was first introduced to me, i laughed at it as well (it didnt help the person arguing for it did a terrible job of it). But when i looked up the proof myself i was convinced. The thing is we know how to turn a repeating decimal into a fraction. I showed it in my first post. It prooves that 0.333... is 1/3rd. Unless you are disputing that multiplying and dividing both sides of an equation by the same value doesnt change its equality... which if you are, you are disagreeing with the most fundamental aspect of algebra.

When you say 'everyone else' you do realise this is an occasion where I'm on the side of what the majority believe, right?

If there is no 9 at the end of 0.9r but yet it is still considered to be a real value, as real and identical in quantity to 1, then it follows that the infinite number of 9s infinitely fail, again and again, to ever reach the value of 1.0r

The proof lies in comprehending a lie in mainstream mathematics that says that 1/3 = 0.3r which is an extreme lie that most children and adults are conned into believing and even marked down in exams for denying. The education system brainwashes us in many ways and I know why pressf4respect asked me what he did. I was too extremely intelligent to find school pleasurable and did loathe it with a passion both socially and academically as it made me look like an idiot for bringing many valid counters to things. There was a direct correlation between how open minded and wise my teacher was and how well we got along (meaning the lower end loathed me as a student).

As for what 1/3 actually is. There is no number, it doesn't exist. It would be 0.3r with a '0333r' at the end of it that itself has a '0333r' at the end of it over and over again, infinitely.

This is then why 0.9r which actually does have 0.3r as a third of its value ends up unequal to 1.0r that has no value at all as a third of its value other than that impossible-to-numerically-describe value that I just described.

Once you fully grasp this, you then will realise a lot else like for instance that 0.9r * 3 = 2/9r7 where the 2 was floating (from the 27) that adds onto the previous 9 before the 7 and zooms to the whole-number place. On the other hand, 1.0r*3.0r = 3.0r that blatantly is not the same number as that 2.9r7

Why do you think you (with no external citation) are without a doubt correct, meanwhile everyone else, and all provided links are wrong? Maybe you should step.back from your certainty and reevaluate your position.

Here is where you are wrong. There is no 9 in the end of 0.9r. There is no end to an infinity. With that, your entire argument collapses.

since you both are struggling, Nemiroff less so, to understand my irrefutable proof, I will cease to engage you. I will simply repeat the sandwich BoP where to disprove one angle, you prove the other true and thus leave 0.9r = 1 an impossible scenario:

EITHER the '9' at the end of 0.9r(ecurring) is never ever reached and the '0' at the end of 1.0r is also never reached
OR the '1' at the end of 0.0r1 is reached and so the difference between the two is an actual value, as well as the '05' at the end of the midpoint 0.9r05 is also reached between 0.9r and 1.
If one is false for the reasons that my opponent stated, it then blackmails them to admit the other is true.

This is irrefutable, absolutely true logic that you cannot just say 'math proof > logical reasoning' without admitting that you're defective in logic, AKA basic IQ.

Also,
Mathematical proofs > logical reasoning.
Logic frequently fails us if we lack data or just spin it the wrong way. Knowledge, facts, and proofs always surpasses logic. The math is irrefutable.

In fact, according to the article all non repeating decimals have a second interpretation using an infinite regression. 3.32 can also be written as 3.31999... they are equal.

"After all the 3s (in 0.333...) there is an imaginery third as a single digit"

What?
Im sorry, there is no after all the 3s, the 3s continue to infinity. So after all the 3s, you have infinitely more 3s to go.

I will go with first choice in that the last 9 is never reached as there are infinite 9s before it. The point is that infinity is not a number, so you will never reach the end. I dont see how that wins the debate for you.

Also, when you x10, you don't get a zero at the end of the repeating decimal. The wiki article explains that in the section titled why some students refuse to accept this *fact*, like you seem to be doing.

Im going to have to agree with respect that you are not fully grasping the concept of infinity. Also education has nothing to do with it. I have a college degree and this still came as a suprise. Not everyone studies math and this question will not come up in law, medicine, or most degree programs.

@RM
If you truly understood what infinite series are, you would naturally know that 0.9r = 1

The formula for infinite series is as follows: S∞ = a/1-r
S∞ is the sum of the infinite series
a is the first term of the series
r is the common ratio of the series

We can break down 0.9r into the following infinite series:
0.9 + 0.09 + 0.009 + 0.0009 + ...

In this case, we are solving for the sum of this infinite series.
0.9 + 0.09 + 0.009 + 0.0009 + ... = S∞
a (the first term) = 0.9
r (common ratio) = 0.1 (each subsequent term is being multiplied by 0.1)
Now we just plug this into the infinite series formula.

S∞ = 0.9/1-0.1
S∞ = 0.9/0.9
S∞ = 1 (Any number divided by itself is 1)

0.9 + 0.09 + 0.009 + 0.0009 + ... = 0.9r
0.9 + 0.09 + 0.009 + 0.0009 + ... = S∞
Therefore, S∞ = 0.9r

S∞ = 0.9r
S∞ = 1
Therefore, 0.9r = 1

QED

I do though. I understand them perfectly. Feel free to read the debate to understand why 0.9 recurring cannot equal 1 and why the idea that 1/3 = 0.3 recurring is actually wrong, because what is actually true is after all the 3's there's an imaginary third as a single digit at the end of it.

I know what an infinite series is. I sandwiched my opponent in both debates into an unwinnable position that 'numerically challenged' voting helped him win with, in terms of official 'win'.

You see, the voters struggled to grasp my very well laid out logic that:
EITHER the '9' at the end of 0.9r(ecurring) is never ever reached and that the '0' at the end of 1.0r is also never reached
OR the '1' at the end of 0.0r1 is reached, as well as the '05' at the end of the midpoint 0.9r05 is also reached between 0.9r and 1.

If one is false for the reasons that my opponent stated, it then blackmails them to admit the other is true. Either way around, I win the debate.

No and no...

I'm not asking to make you feel bad.

My highest level of education has nothing to do with this.

The reason I asked you the question is because you don't seem to understand the concept of infinite series.

Do you ask every member to reveal IRL achievements that would help you to narrow them down?

Are you trying to ask only me that one question because you want me to feel bad when your highest level of education is high school?

Stop worrying about others, get busy judging yourself and improving yourself.

@RM
What obsession?
I was asking an honest question.
I'm not stalking you either, stop being delusional.

Get over your obsession with me and stalk someone else.

@RM
What is the highest level of education you completed?