Mathematical curiosity

intergamer said:

If you subtract 0.9999... from 10, you get 9. 0.999... and 1 are representations for the same number, just as (2+1), (1+2), and 3, are representations for the same number.

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Oh, okay. So 0.999.... =1 because 0.999...=1.

Thanks.

if c = 0.999..., then surely you believe that 10c = 9.999...?

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Of course.

and then you believe that 10c-c = 9

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You're saying 9c=9 so c=1. So you're really just repeating yourself without explaining anything. You just jumped from 0.999.... to 1. I understand that 0.9999...is infinite, but I don't understand why that means it has to be equal to 1. In order to understand what you just said there, you have to already believe that 0.9999.... is equal to 1, which I do not.

Nonono, hold on. I see. 0.11111... is equal to 1/9 and 0.11111....X 9 = 0.999... and 1/9 X 9 = 1. I got it.


See. All you had to do was use fractions. It's much easier to explain that way.

vaxer said:

by writing this you are saying that 10c-c != 9c meaning that 1 != 1
So you got something wrong (9 x 0.9999... != 8.9999... it's a misconception).

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I just wrote somthing completly wrong here, indeed 9 x 0.999... = 8.999... = 9. You tend to forget that the dots are here...

I am not a matematichian, I am engineer. We were told that an error in a final caculation is alowed up to 5% of the correct value.
So this whole argument is kinda silly to me.

PS:
you broke a math rule there, consult your math proffesor

Gustav said:

Oh, okay. So 0.999.... =1 because 0.999...=1.

Thanks.


Of course.
You're saying 9c=9 so c=1. So you're really just repeating yourself without explaining anything. You just jumped from 0.999.... to 1. I understand that 0.9999...is infinite, but I don't understand why that means it has to be equal to 1. In order to understand what you just said there, you have to already believe that 0.9999.... is equal to 1, which I do not.

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Listen bro, I gave the more theoretical explanations, you just don't understand them. You can rest assured that you are not correct in your foolish beliefs. FWIW, I am a mathematician, and a good one. I hope for your sake that you are just trolling.

qafir said:

(look, i'm being a very bad boy)

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there is one thing that YOU don't understand. how may i put it? it's like... uhm... well: maths was my primary subject at school for 13 years. after this, i went right on studying maths at university. and the last time i "picked up a calculus book" isn't fifteen years ago but something like a week and a half.

and now you smart man believe that you could tell me that 0.(9) isn't equal to 1?

you might want to reconsider. it's like you were on war with the rest of the mathematical world.

but let me give this another try.

every number with a recurring decimal can be displayed as a fraction number. now this leads us to a series of questions:

- what fraction other than 1 equals 0.(9)?
- what's the difference "1 - 0.(9)"?
- how can a number move, approach, ...?

i hope i've made myself clear although me is man who speak german and you is man who speak english. and although me english be bad and you english be good.

all me seen from you so far is that you say "all of you people not speak english good". you speak english good. is there anything else that you is good at? you ever use you brain for something else than spelling?

me woulds like very many much to find out. because german-jay thinks that perhaps you have no idea about rest of big big world. for example maths.

me is subhuman because me is no good at english. is you great superhero because you can speak you native language?

german-jay say thanks for answering questions that he is too stupid to answer on me own.

Jay,

I've started a Why I Hate Qafir thread. Please limit your attacks to that thread.

First off, I already explained in detail how numbers (functions, actually) "approach" zero, or infinity, or any other defined or undefined point. Please refer to my above definition of a one-dimensional number line. I actually wanted to double-check myself yesterday, and I pulled out an English Calculus text. It uses the term "approaches." Any time you graph a function, you use "motion" words to describe following the function along the graph. This was not an insult to your english, Jay. I was merely pointing out that you've gotten huffy about a semantic word or two here, when it's really just a cultural different.

Second, 0.999! never equals 1. They do not have the same definition. But for all intents and purpose, they are TREATED as the same thing. The test of this is simple. Please refer to my above suggestion that you insert the defined value of c (0.9999999...) back into the equation to verify that the solution is correct. If you do so, you find that while in the original proof, 10c-c=9c=9, that conclusion is not verified if you multiply (9 x 0.99999999...). You always get 8.999... UNTIL you arbitrarily choose a decimal place and round to that point. THEN you get the answer 9. My point, and I think we've all gone on long enough, is that the original proof is a way of simplifying an equations, of reducing an infinitely repeating variable (hard to use in equations) to it's nearest approximate equal. But that simplification is an anomaly, not a true equality.

I agree, in the original proof presented, 10c-c = 9. This is a mathematical simplification. Please see my above comparison to treating pi as a three digit number for calculations when we all know it's a randomly repeating infinite decimal. We do not use these simplifications (rounded-off numbers) because they ARE equal. We use them because there is no other way of handling complex equations.

So come on...You know as well as I do that you don't object to my math. You hate me personally. That's why you singled me out and started your original post by calling me an idiot. And now you don't have to masquerade your hatred behind puffed pseudo-intellectually crap. You have an open invitation to vent it fully in the Why I Hate Qafir thread.

But leave me alone in the other threads in this forum. Interact with me like a normal human being, and we can avoid these tedious interactions that get WAY off topic.

Q

qafir said:

You always get 8.999... UNTIL you arbitrarily choose a decimal place and round to that point. THEN you get the answer 9.

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You never arbitrarily choose a decimal place and round to that point, if so the equality wouldn't stand. Your problem is that you believe that the value of a convergent serie is an approximation, not the actual value.

intergamer said:

Listen bro, I gave the more theoretical explanations, you just don't understand them. You can rest assured that you are not correct in your foolish beliefs. FWIW, I am a mathematician, and a good one. I hope for your sake that you are just trolling.

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Sure you are, kid.

What am I not correct about here? You did repeat yourself. Your explanations required the one being explained to to already believe what you were trying to explain. So your entire big post was obsolete. It's like defining a word and using that word in the definition. Understand?

" It's like defining a word and using that word in the definition."

Then, if I may be pedantic for just a second () I believe the word you might be looking for is "redundant", not "obsolete".

Redundant would be a better word. Redundant and useless was the explanation. Obsolete makes it sound like it was once useful.

qafir said:

First off, I already explained in detail how numbers (functions, actually) "approach" zero, or infinity, or any other defined or undefined point.

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numbers or functions? because the way that 0.(9) is created has nothing to do with a function, son. it's a progression. which is something entirely different. a progression can represent a number if it converges to a limit (which then will be the represented number). a function is something entirely different. in some cases, you can convert a progression into a function but this would in fact move it even further away from the number-thing.

you better take your calculus book again and check the words you want to use.

qafir said:

I actually wanted to double-check myself yesterday, and I pulled out an English Calculus text. It uses the term "approaches."

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i'm sure the word "approaches" will appear somewhere in this book. but i'm just as sure that it isn't applied to the word "number". if so, i would like to see a scan.

qafir said:

Any time you graph a function, you use "motion" words to describe following the function along the graph.

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okay and where in this whole problem do you see a function?

qafir said:

Second, 0.999! never equals 1.

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i know. the difference is 0.0001. and what's the difference between 0.(9) and 1? because we aren't talking about 0.999. at least i'm not. and vaxer surely wasn't, either.

qafir said:

Second, 0.999! never equals 1. They do not have the same definition. But for all intents and purpose, they are TREATED as the same thing. The test of this is simple. Please refer to my above suggestion that you insert the defined value of c (0.9999999...) back into the equation to verify that the solution is correct. If you do so, you find that while in the original proof, 10c-c=9c=9, that conclusion is not verified if you multiply (9 x 0.99999999...). You always get 8.999... UNTIL you arbitrarily choose a decimal place and round to that point. THEN you get the answer 9.

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this is a logical fallacy. if you put "c" in and get "c" out, it doesn't mean that "c" isn't the very same thing as one. 8.(9) is the same thing as 9.

if you "round" this means making one number a different one. a "different" number must have a "difference" to the original number. so what is the difference?

qafir said:

I agree, in the original proof presented, 10c-c = 9. This is a mathematical simplification. Please see my above comparison to treating pi as a three digit number for calculations when we all know it's a randomly repeating infinite decimal.

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what you refuse to understand is that when you round pi, you will get:

"rounded pi"-pi=x and x>0, no matter at what decimal you round pi.

when you say:

0.(9)-1=x then x=0.

qafir said:

I We do not use these simplifications (rounded-off numbers) because they ARE equal. We use them because there is no other way of handling complex equations.

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i don't know who "we" are, but *i*, personally, as a maths student, never use rounded numbers. the reason for this is simple: i don't calculate with real numbers anymore. most of the time everything is written in variables. you can "round" in physics. not in maths. and if i write 0.(9)=1 this doesn't mean i'm too lazy to make a difference. it is absolutely one and the same thing. that 0.(9) LOOKS different to 1 mostly is a flaw of decimal notation.

qafir said:

So come on...You know as well as I do that you don't object to my math. You hate me personally.

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sure. your maths is correct. everybody who disagrees must be a hater. earth IS flat.

i've given you three simple questions. they were:

Jay R. Zay said:

- what fraction other than 1 equals 0.(9)?
- what's the difference "1 - 0.(9)"?
- how can a number move, approach, ...?

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you didn't answer any single one of them. why? because i hate you? or because you can't?

i would like to add a fourth question:

- is or isn't 0.(3) = 1/3 ?

answer them without contradicting yourself (and without talking about something as unrelated as "functions") and you're done. okay?

if you instead prefer to talk about everything OTHER than these three or four questions, i believe we both can agree that i am right and you are wrong. and, last but not least, for this reason: before you start making fun of anybody's english (mine, rae's, ...), better learn maths. because actually right now you are giving a rather ridiculous show. and, as intergamer chose to say, you better aren't serious about this.

vaxer said:

This will probably going bore everybody to death but?

Normally, you?d think 0.9999? (with an infinit number of 9s) would be smaller then 1 in an inifitly small way. But no, they equate exactly! 1 = 0.9999?

The most simple demonstration is :
c = 0.9999?
10c = 9.9999?
10c ? c = 9.9999? - 0.9999?
9c = 9
c = 1
meaning : 1 = 0.9999?

Funny how things arn?t what they look like.

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c = 0.999...
10c = 9c + c = [ 9 x (0.999...) ] + 0.999...
10c - c = ( 9c + c ) - c = [ 9 x (0.999...) ] + 0.999... - 0.999...
9c = 9 x (0.999...)
c= 9 x ( 0.999...) / 9 = 8.999.../9
c =0.999...
We did not end with c=1

Funny how things aren't what they look like.

The original proof is a simplified mathematical model designed to reduce the unfathomable/incalculable infnite repeating series to a defined, fixed-digit integer. We only do this because our number systems and mathematics itself breaks down when we approach these numbers.

You can't use fixed-digit thinking or rules to describe infinite progressions. Much like you can't use newtonian physics (good enough to land a man on the moon) to describe what happens at the event horizon of a black hole or what happens when mass accellerates to the speed of light or quantum leaps.

qafir said:

You can't use fixed-digit thinking or rules to describe infinite progressions.

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ironically, this happens to be the very reason why i am right and you are wrong.

and, concerning your "proof" above, "we did not end with c=1" indeed, but we did not end with c≠1, either. actually, we didn't do anything interesting with c that could tell us about its precise value. which makes it a rather worthless bunch of mathematical constructions. if you put a variable into something, you might get it out again the same way. but just because x*10/10+20-20=x, this doesn't mean that x can't be 1.

~~~

and could we, pehaps, pretty please stop using "999..." to describe perdiods and "x" to describe a multiplication? x is a letter (maybe a variable?) and "999..." doesn't mean anything at all. i wonder why our chief maths expert isn't aware of the correct notations and still writes on an elementary school level? flawed as my english might be, i think it's above elementary school level, isn't it?

Gustav said:

Sure you are, kid.

What am I not correct about here? You did repeat yourself. Your explanations required the one being explained to to already believe what you were trying to explain. So your entire big post was obsolete. It's like defining a word and using that word in the definition. Understand?

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You want to contest my mathematical background? (Hint: don't). Regardless of what you believe, you're the one who doesn't understand, because 0.999...=1. Seriously... look it up in an encyclopedia or something. Every demonstration I gave is completely accurate and a sufficient proof. You (and qafir) seem to be arguing the definition of 0.999..., which is very fruitless. If 0.999... does not equal 1, then what number is in between them? Two nonequal numbers must have a positive and finite distance.

calm down. read this?

Gustav said:

Nonono, hold on. I see. 0.11111... is equal to 1/9 and 0.11111....X 9 = 0.999... and 1/9 X 9 = 1. I got it.


See. All you had to do was use fractions. It's much easier to explain that way.

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Jay R. Zay said:

calm down. read this?

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that post was before the post questioning my mathematical background, and it's also ridiculous to suggest that this fractional method is any better than the method vaxer gave (it actually requires more assumptions).

OK, Jay

sure. your maths is correct. everybody who disagrees must be a hater. earth IS flat.

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No, I don't assert that since you disagree with me, you must be a hater. You're a hater because you're hateful. Until you jumped in, this was a peaceful thread. You're the one who chose as his opening line, "but i would like to take this opportunity to call you an idiot." You may be right about the math, and I may be wrong. That's something we can discuss. Who knows, maybe you have a world to teach me. But "idiot" is harsh and was entirely unwarranted.

Let's not forget, you concluded your last post with

before you start making fun of anybody's english (mine, rae's, ...)

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. Jay, don't you see how this has nothing to do with math? You're caustic to me because you're angry about unrelated, off-topic posts from other threads. Seriously, leave me in peace, and I'll do the same to you. Save your venom for honest attacks in the Why I Hate Qafir thread. Be a man.

As for the rest, I have no more time to debate this point, so I'll concede: You're right mathematically and I'm wrong. OK?

But you need to seriously think about why the heck you and your cronies have it in for me. I didn't start the hatred outside this thread any more than I started it here. It's not my fault if you're caustic and sarcastic yet too big a baby to take ribbing or sarcasm in return.

intergamer said:

that post was before the post questioning my mathematical background, and it's also ridiculous to suggest that this fractional method is any better than the method vaxer gave (it actually requires more assumptions).

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it's easier to understand if you don't have the mathematical background to see the problem as it really is. it's no real mathematical proof but i think it's more simple and more intuitive.

anyway, i think you both agree about the facts.

qafir said:

OK, Jay



No, I don't assert that since you disagree with me, you must be a hater. You're a hater because you're hateful. Until you jumped in, this was a peaceful thread. You're the one who chose as his opening line, "but i would like to take this opportunity to call you an idiot." You may be right about the math, and I may be wrong. That's something we can discuss. Who knows, maybe you have a world to teach me. But "idiot" is harsh and was entirely unwarranted.

Let's not forget, you concluded your last post with . Jay, don't you see how this has nothing to do with math? You're caustic to me because you're angry about unrelated, off-topic posts from other threads. Seriously, leave me in peace, and I'll do the same to you. Save your venom for honest attacks in the Why I Hate Qafir thread. Be a man.

As for the rest, I have no more time to debate this point, so I'll concede: You're right mathematically and I'm wrong. OK?

But you need to seriously think about why the heck you and your cronies have it in for me. I didn't start the hatred outside this thread any more than I started it here. It's not my fault if you're caustic and sarcastic yet too big a baby to take ribbing or sarcasm in return.

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four questions. remember?

anything left for you to say about 0.(9) and 1? no? ah.

i don't think we need to discuss your personality after we've got this right. anybody who is interested in seeing the way you think you could argue can do so right here. i don't need to hate you. i've seen many people who tried to be tough bad boys. and what else happes on this forum is no longer my business. i just found your amusing arrogance in other places a very good comparison. you might disagree though.

intergamer said:

You want to contest my mathematical background? (Hint: don't). Regardless of what you believe, you're the one who doesn't understand, because 0.999...=1. Seriously... look it up in an encyclopedia or something. Every demonstration I gave is completely accurate and a sufficient proof. You (and qafir) seem to be arguing the definition of 0.999..., which is very fruitless. If 0.999... does not equal 1, then what number is in between them? Two nonequal numbers must have a positive and finite distance.

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Oh, that's what you thought was foolish. Well, it was kind of since I was wrong. But wouldn't it be more foolish to just believe whatever you say at the drop of a hat without understanding it first?

Look at my post from yesterday that was made just five minutes after my post before it. Since then it has been my understanding that 0.999... does equal 1. I found it much easier to understand using fractions. And for future reference, I think that would be a better way to explain it to somebody who doesn't know.