Eff this, philly mike is an idi0t, ask zdunklee.

[dingdongyo]

actually it really doesn't matter to me, for a few reasons, 1 I don't care what mathematicians or math majors have to say unless it has an actual application. .999... = 1 has no bearing, and i still don't believe it is true. Even if i were to go with this what would it matter?

didn't you create this thread?

if you choose to follow your own rules of math, then we have found the disconnect and you're right: there's no reason to continue discussing it.

I was tutoring a boy yesterday and I tried to tell him about imaginary numbers. He told me all numbers are imaginary. What is x? That is a letter in the alphabet.

This might take a while...

in freshman year in high school, i was in a computer programming class, and i remember cracking up when some kid asked the teacher for help with where his program was failing:

"ok, so 'fart' gets 'fart' + 1..."

variables are fun.

[taekahn]

I was tutoring a boy yesterday and I tried to tell him about imaginary numbers. He told me all numbers are imaginary. What is x? That is a letter in the alphabet.

This might take a while...

Don't be so quick to correct the boy, every number does have an imaginary part. 1+0i.

[Allyson]

I was tutoring a boy yesterday and I tried to tell him about imaginary numbers. He told me all numbers are imaginary. What is x? That is a letter in the alphabet.

This might take a while...

Don't be so quick to correct the boy, every number does have an imaginary part. 1+0i.

Oh good point. In that case every number has infinite parts. 1 + 0i + 0 + 0*2 + 0x + ...

And here we go again.

[Philly Mike]

I was tutoring a boy yesterday and I tried to tell him about imaginary numbers. He told me all numbers are imaginary. What is x? That is a letter in the alphabet.

This might take a while...

Don't be so quick to correct the boy, every number does have an imaginary part. 1+0i.

hey shouldn't you be working with titles or something, instead of writing on a message board??? isn't that against company policy lol

[taekahn]

Sorry, but i was just implying that maybe the boy was trying to say that all numbers are complex in the only way he knew how to phrase it.

[taekahn]

Don't be so quick to correct the boy, every number does have an imaginary part. 1+0i.

hey shouldn't you be working with titles or something, instead of writing on a message board??? isn't that against company policy lol

Maybe i'm home sick, or perhaps this is part of your master plan to get me fired so i have to hang out with you.

[uhohspagettio]

I agree with Allison on this and not because she is the hottest chick on the board, here is my example. When I want to order something at McDonalds I will say something along these lines, "I would like the #1 Value meal with a Coke." I do not say "I would like the #.999 Value meal with a Coke."

^so what, that doesn't have anything to do with it, 1 is easier to say, just like 1/2 is the preferred representation of 256/512.

Holy Ess! Are you one of those people that when asked for directions will say "Drive 1.4532 miles and make a 90 degree turn to the north, continue on for 275 yards or 825 feet and make 90 turn to the west....etc. etc."

[Philly Mike]

actually it really doesn't matter to me, for a few reasons, 1 I don't care what mathematicians or math majors have to say unless it has an actual application. .999... = 1 has no bearing, and i still don't believe it is true. Even if i were to go with this what would it matter?

as far as the you never see .50 off in stores. Well you could have fooled me because they say 50% off which is .50 just with a % on one end instead of the . on the other. I have never seen them say "3/4 off in this insane offer" usually it is 75% off.

I was saying fractions were simpler anyway, so that has no bearing.

and tae, as far as nullility goes, well you and lee here can probably have a brain-dead conversation about that. .999... = 1 i can at least see why people believe it, but stating that 0 actually has value, well that is just plain retarded work that only a minger of high caliber could ever create.

They believe 0.999... = 1 only because that is how the real numbers have been defined, thus if you are talking about the real number system the two values are always equal. However there are number systems out there in which 0.999... =! 1, such as the p-adic numbers, but that would be a different topic altogether.

This is much the same idea that there is Euclidean Geometry(which is the geometry that everyone recognizes) and Spherical Geometry in which nothing is ever parallel and there are no lines.

If you really want to get into some crazy math discussion, how about we talk about the fact that all math done from the 19th century on was based upon the work of someone who never existed? ???

the biggest thing i don't get is how you could say .999... is a real number when it is an infinite decimal. there is no real to it. it can not be used with real life applications, it would need to be rounded up when used just like if you were to try to do something with the string .444... you would do something like x .444445 to be able to get the closest estimation. the same goes with the .999... because you cant really use it in the application that numbers are supposed to represent a value of something.

I mean hell, if you multiply .999... by 10 you get 9.999 you multiply it by 1 it equals .999...
there is no changing that. if you multiply 10 and 1 you get 10. showing .999... as anything else is just rounding to the nearest number.

[zdunklee]

^so what, that doesn't have anything to do with it, 1 is easier to say, just like 1/2 is the preferred representation of 256/512.

Holy Ess! Are you one of those people that when asked for directions will say "Drive 1.4532 miles and make a 90 degree turn to the north, continue on for 275 yards or 825 feet and make 90 turn to the west....etc. etc."

No, I am just saying that every single number has multiple representations and even in math the preferred way to write them is whatever one is the simpliest, which is why if you do get a number like 0.999... you write it as a 1.

[Philly Mike]

Holy Ess! Are you one of those people that when asked for directions will say "Drive 1.4532 miles and make a 90 degree turn to the north, continue on for 275 yards or 825 feet and make 90 turn to the west....etc. etc."

No, I am just saying that every single number has multiple representations and even in math the preferred way to write them is whatever one is the simpliest, which is why if you do get a number like 0.999... you write it as a 1.

Kind of like if you get 0.444... you write 0.45

[Howie Feltersnatch]

No, I am just saying that every single number has multiple representations and even in math the preferred way to write them is whatever one is the simpliest, which is why if you do get a number like 0.999... you write it as a 1.

Kind of like if you get 0.444... you write 0.45

no, you would write .44 as 5 is the trigger to round up.

[zdunklee]

They believe 0.999... = 1 only because that is how the real numbers have been defined, thus if you are talking about the real number system the two values are always equal. However there are number systems out there in which 0.999... =! 1, such as the p-adic numbers, but that would be a different topic altogether.

This is much the same idea that there is Euclidean Geometry(which is the geometry that everyone recognizes) and Spherical Geometry in which nothing is ever parallel and there are no lines.

If you really want to get into some crazy math discussion, how about we talk about the fact that all math done from the 19th century on was based upon the work of someone who never existed? ???

the biggest thing i don't get is how you could say .999... is a real number when it is an infinite decimal. there is no real to it. it can not be used with real life applications, it would need to be rounded up when used just like if you were to try to do something with the string .444... you would do something like x .444445 to be able to get the closest estimation. the same goes with the .999... because you cant really use it in the application that numbers are supposed to represent a value of something.

I mean hell, if you multiply .999... by 10 you get 9.999 you multiply it by 1 it equals .999...
there is no changing that. if you multiply 10 and 1 you get 10. showing .999... as anything else is just rounding to the nearest number.

Not true, and you don't round .444... to .4445 where they hell did you learn to round? .4444... = 4/9 and that is not an estimation it is the exact value of .4444..., simply put they are called RATIOnal, which strictly means a ratio of two integers, which is why they are represented by a fraction in the first place.

The real numbers is the name of the system, called such in a response to the imaginary numbers which were found and named first. It doesn't translate literally to mean real.

[zdunklee]

If you really want to get into the history of math I can go there. But here is one of the best explainations as to why what you are thinking is wrong. From this website: http://qntm.org/?pointnine

Common counter-arguments and my responses

"0.9999... and 1 are obviously different numbers."
Not good enough. Intuition counts for nothing. In mathematics, proof is everything, and "obvious" means "a proof springs immediately to mind". Please PROVE that 0.9999... and 1 are not equal. Without proof, no hunch, feeling, or intuition is worth anything.

"1 and 0.9999... are written differently, therefore they are different numbers."
There are many ways of writing ANY number. You could write 1/1, or 2/2, or 9/9, or 2-1, or 1.0, or 1.00, or 1.0000... or any number of other expressions, and all of them ultimately have the same meaning, "one".

"0.9999... is a concept, not a number."
All numbers are concepts. Some numbers, like 1, have stronger links to reality than others, but we are looking at mathematics here, not the real world. If you're going to throw away numbers which can't concretely exist, then you're throwing away pi, e, i, zero, and, frankly, almost all of mathematics.

"There is a rounding error. 0.9999... and 1 are approximately equal."
Do you see any rounding or approximation going on around here? That only happens when you stop counting after a certain number of decimal digits. But I have kept and counted every single one of the infinitely many decimal digits in my proofs. No rounding, no error.

"0.9999... gets closer and closer to 1, but never reaches it."
Closer and closer? How can it be getting closer and closer? It's one number! Try the limit argument, above.

"0.9999... is a decimal representation of infinity, not a number."
Well, how come it's DEFINITELY bigger than 0.5 and smaller than 2? Just because something has infinitely many pieces doesn't mean it's infinite. Zeno figured this out 2500 years ago.

"Humans can't comprehend infinity, and not being able to comprehend infinity means you can't do mathematics with it."
This statement is wrong on many levels. When you say humans cannot comprehend infinity, you are quite likely projecting your own inability to comprehend infinity onto everybody else in the world, among them many thousands of mathematicians who are perfectly capable of sitting down and dealing with infinite values in a sane and rational fashion. It may impossible to literally conceive of infinite values - whatever formal definition such conception could possibly have - but that does not and never will stop mathematicians from dealing with them. Mathematics is all about rules. Mathematicians have discovered that there are rules for dealing with infinity. These rules are perfectly consistent with our rules for dealing with other numbers, and given a little time you could probably learn to apply them yourself.

In case the connection isn't clear, what is true of infinite values is equally true of infinite decimal expansions. There are rules and procedures and they work and give meaningful results. See "The Real Proof" above for a relatively tame glimpse of this, which is actually a vast region of mathematics known as "analysis", naturally based on rock-solid fundamental axioms.

"My mate/my dad/my mathematics teacher/Professor Stephen Hawking told me that 0.9999... and 1 were different numbers."
They were wrong. In science, credentials are as worthless as intuition (above). Proof is everything.

"But they proved it, too!"
The proof was fallacious. Send it to me and I'll show you why.

"I still don't believe it, and I'm entitled to my own opinion."
Mathematics is unlike regular science in that we can actually prove things, permanently, for real, instead of just finding increasing amounts of evidence supporting our hypotheses. That's why we have what we call "theorems" instead of theories. That point nine recurring equals one is just such a theorem (although it's so easy that it's barely worth the name). You aren't in a position to argue or debate about it. It's a fact. Your opinion is wrong.

You are entitled to be wrong, I suppose. However, if you are unable to admit that you are wrong when you have been proven wrong, then you have no business taking part in a mathematical discussion or pretending that you know anything about mathematics. Therefore, I must request that you please distance yourself from any future discussions that you may encounter on this topic, so that those who do want to learn, rather than just promote an ideology, can do so

[Philly Mike]

the biggest thing i don't get is how you could say .999... is a real number when it is an infinite decimal. there is no real to it. it can not be used with real life applications, it would need to be rounded up when used just like if you were to try to do something with the string .444... you would do something like x .444445 to be able to get the closest estimation. the same goes with the .999... because you cant really use it in the application that numbers are supposed to represent a value of something.

I mean hell, if you multiply .999... by 10 you get 9.999 you multiply it by 1 it equals .999...
there is no changing that. if you multiply 10 and 1 you get 10. showing .999... as anything else is just rounding to the nearest number.

Not true, and you don't round .444... to .4445 where they hell did you learn to round? .4444... = 4/9 and that is not an estimation it is the exact value of .4444..., simply put they are called RATIOnal, which strictly means a ratio of two integers, which is why they are represented by a fraction in the first place.

The real numbers is the name of the system, called such in a response to the imaginary numbers which were found and named first. It doesn't translate literally to mean real.

Which brings me back to the point that the fraction is just the division of the numbers not showing the actual answer because it is simpler it would be the same as saying instead of writing the number 2 i will just write 1+1, they mean the same thing but 1+1 is the incomplete way of doing it. the difference is that with fractions and infinite decimals the fraction is just showing a rounded version of the infinite because it is easier.

[zdunklee]

Not true, and you don't round .444... to .4445 where they hell did you learn to round? .4444... = 4/9 and that is not an estimation it is the exact value of .4444..., simply put they are called RATIOnal, which strictly means a ratio of two integers, which is why they are represented by a fraction in the first place.

The real numbers is the name of the system, called such in a response to the imaginary numbers which were found and named first. It doesn't translate literally to mean real.

Which brings me back to the point that the fraction is just the division of the numbers not showing the actual answer because it is simpler it would be the same as saying instead of writing the number 2 i will just write 1+1, they mean the same thing but 1+1 is the incomplete way of doing it. the difference is that with fractions and infinite decimals the fraction is just showing a rounded version of the infinite because it is easier.

What the hell man, how many times do I have to say this: FRACTIONS ARE NOT ROUNDED! The only way they are rounded is if you are incapable of working with infinity and round off the decimal expansion at some point in your own head, which is apparently the case. Even Calculators do not round off fractions...

In mathematics, real mathematics not the mathematics in your head, if a number is rational it is always taken as a fraction or its whole number representation, it is never taken as the decimal because the decimal would lead to bad calculations not being able to extend it to infinity.

[Philly Mike]

Which brings me back to the point that the fraction is just the division of the numbers not showing the actual answer because it is simpler it would be the same as saying instead of writing the number 2 i will just write 1+1, they mean the same thing but 1+1 is the incomplete way of doing it. the difference is that with fractions and infinite decimals the fraction is just showing a rounded version of the infinite because it is easier.

What the hell man, how many times do I have to say this: FRACTIONS ARE NOT ROUNDED! The only way they are rounded is if you are incapable of working with infinity and round off the decimal expansion at some point in your own head, which is apparently the case. Even Calculators do not round off fractions...

In mathematics, real mathematics not the mathematics in your head, if a number is rational it is always taken as a fraction or its whole number representation, it is never taken as the decimal because the decimal would lead to bad calculations not being able to extend it to infinity.

the fraction itself isn't rounded, but it represents the rounded infinite decimal.

[Howie Feltersnatch]

this should solve all the arguments


http://www.hoc.org.uk/gallery/funny/math.jpg

warning boobs (holstered)

[zdunklee]

What the hell man, how many times do I have to say this: FRACTIONS ARE NOT ROUNDED! The only way they are rounded is if you are incapable of working with infinity and round off the decimal expansion at some point in your own head, which is apparently the case. Even Calculators do not round off fractions...

In mathematics, real mathematics not the mathematics in your head, if a number is rational it is always taken as a fraction or its whole number representation, it is never taken as the decimal because the decimal would lead to bad calculations not being able to extend it to infinity.

the fraction itself isn't rounded, but it represents the rounded infinite decimal.

Only in your head, it does not to any mathematicians or claculators. Tell me exactly where 1/9 is rounded off, and I'll show you that the next place has a number in it.

[Philly Mike]

this should solve all the arguments


http://www.hoc.org.uk/gallery/funny/math.jpg

I'm surprised it didn't have a cow in the pic.

[Philly Mike]

the fraction itself isn't rounded, but it represents the rounded infinite decimal.

Only in your head, it does not to any mathematicians or claculators.

If the fraction represented the actual number then you would never be able to multiply it because you have to multiply every number in behind the decimal and that would just go on forever considering it is an infinite string. so the cut off has to be somewhere.

[zdunklee]

Only in your head, it does not to any mathematicians or claculators.

If the fraction represented the actual number then you would never be able to multiply it because you have to multiply every number in behind the decimal and that would just go on forever considering it is an infinite string. so the cut off has to be somewhere.

Jesus, this is simply not true, a fraction IS the number and when you multiply the fraction it takes into account the entire number. Please read up on the definitions of the rational numbers before you start arguing about something you obviously do not understand or comprehend.


BTW just in case you didn't realize it the phrase you used of rounded infinite decimal makes no sense, you can't round an infinite decimal and still have the same number you started with.

[dingdongyo]

this should solve all the arguments


http://www.hoc.org.uk/gallery/funny/math.jpg

crap, didn't see boobs coming.

"hello IT officer..."

i will be studying this later, don't get me wrong.

[Philly Mike]

you can't round an infinite decimal and still have the same number you started with.

exactly, which is why .999... is a separate number, because the only way to make it 1 is to round up to the nearest finite number.

oh and by the way, i was looking back at this whole argument and there is something that doesn't make sense in your original argument with this.

x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

this is incorrect
this is how it should be

x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 8.9999...
x = 0.9999...

so even your own original statement shows no proof.

[Howie Feltersnatch]

Set a value for x.

If x = 0.9999~

then 10x = 9.9999~

and 10x - x = (9.9999~ - 0.9999~) = 9

so 9x = 9

and x = 1.

[zdunklee]

you can't round an infinite decimal and still have the same number you started with.

exactly, which is why .999... is a separate number, because the only way to make it 1 is to round up to the nearest finite number.

oh and by the way, i was looking back at this whole argument and there is something that doesn't make sense in your original argument with this.

x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

this is incorrect
this is how it should be

x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 8.9999...
x = 0.9999...

so even your own original statement shows no proof.

For the first part, no this is not true, you do not round 0.999... ever and I don't get what you do not understand, please look up the definitons of Real and Rational numbers like I suggested. Unlike most science math is not a debatable subject, as proofs are concrete and opinion means absolutely nothing.

As for the second, this is another example of you not being able to think in terms of infinity. I want you to SHOW me why 9.999... - 0.999... = 8.999, it doesn't ever. I can clearly see that you don't use math very often... just by the terrible mistakes you are making that are simple to other here as well.

BTW that is one of the smiplest proofs I can give you, if you want me to give you the real calculus based proof I can do that, but I don't think you will understand the first line of it.

[Philly Mike]

exactly, which is why .999... is a separate number, because the only way to make it 1 is to round up to the nearest finite number.

oh and by the way, i was looking back at this whole argument and there is something that doesn't make sense in your original argument with this.



this is incorrect
this is how it should be

x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 8.9999...
x = 0.9999...

so even your own original statement shows no proof.

For the first part, no this is not true, you do not round 0.999... ever and I don't get what you do not understand, please look up the definitons of Real and Rational numbers like I suggested. Unlike most science math is not a debatable subject, as proofs are concrete and opinion means absolutely nothing.

As for the second, this is another example of you not being able to think in terms of infinity. I want you to SHOW me why 9.999... - 0.999... = 8.999, it doesn't ever. I can clearly see that you don't use math very often... just by the terrible mistakes you are making that are simple to other here as well.

where are you getting i said 9.999... - 0.999... = 8.999...

last time i checked the statement x=0.999... then 9x means 9 times 0.999... and that would equal 8.999 the same way 10x equals 9.999...

I do enough math to understand how to multiply
you told me to start using that calculator thingy. Why not try using it yourself?

[zdunklee]

For the first part, no this is not true, you do not round 0.999... ever and I don't get what you do not understand, please look up the definitons of Real and Rational numbers like I suggested. Unlike most science math is not a debatable subject, as proofs are concrete and opinion means absolutely nothing.

As for the second, this is another example of you not being able to think in terms of infinity. I want you to SHOW me why 9.999... - 0.999... = 8.999, it doesn't ever. I can clearly see that you don't use math very often... just by the terrible mistakes you are making that are simple to other here as well.

where are you getting i said 9.999... - 0.999... = 8.999...

last time i checked the statement x=0.999... then 9x means 9 times 0.999... and that would equal 8.999 the same way 10x equals 9.999...

I do enough math to understand how to multiply
you told me to start using that calculator thingy. Why not try using it yourself?

You said that when you changed the numbers in the proof, that is what that is a proof, if you change the numbers you are changing the proof.

I know that if you multipy 9* 0.999 it equals 8.9999... which in turn = 9. But that is NOT what I did in the proof. I didn't ever multiply 9 * 0.9999 ever in the proof.

The 9x = 9 comes from the previous step in which 10x-x - 9.999... - 0.999..., that is what a proof is, it is logical steps that follow from one to the next.

[dingdongyo]

where are you getting i said 9.999... - 0.999... = 8.999...

10x - x = 9.9999... - 0.9999...
9x = 8.9999...

if this doesn't prove to you that you are confusing yourself, i don't know what to tell you

[Philly Mike]

where are you getting i said 9.999... - 0.999... = 8.999...

last time i checked the statement x=0.999... then 9x means 9 times 0.999... and that would equal 8.999 the same way 10x equals 9.999...

I do enough math to understand how to multiply
you told me to start using that calculator thingy. Why not try using it yourself?

You said that when you changed the numbers in the proof, that is what that is a proof, if you change the numbers you are changing the proof.

I know that if you multipy 9* 0.999 it equals 8.9999... which in turn = 9. But that is NOT what I did in the proof. I didn't ever multiply 9 * 0.9999 ever in the proof.

The 9x = 9 comes from the previous step in which 10x-x - 9.999... - 0.999..., that is what a proof is, it is logical steps that follow from one to the next.

WTF are you talking about???

x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

that is exactly what you wrote
you just said yourself that 9*0.999... would be 8.999...

the reason you did the statement was to show how you make it = 1 but if the math is done properly you prove that 0.999... = 0.999... and that's it.

[zdunklee]

Ok Mike, since you clearly can't comprehend that proof, here is the real calculus based proof, good luck...

[zdunklee]

You said that when you changed the numbers in the proof, that is what that is a proof, if you change the numbers you are changing the proof.

I know that if you multipy 9* 0.999 it equals 8.9999... which in turn = 9. But that is NOT what I did in the proof. I didn't ever multiply 9 * 0.9999 ever in the proof.

The 9x = 9 comes from the previous step in which 10x-x - 9.999... - 0.999..., that is what a proof is, it is logical steps that follow from one to the next.

WTF are you talking about???

x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

that is exactly what you wrote
you just said yourself that 9*0.999... would be 8.999...

the reason you did the statement was to show how you make it = 1 but if the math is done properly you prove that 0.999... = 0.999... and that's it.

No it doesn't in a proof you have to get the next step from the previous, I am not multiplying 9*0.999... anywhere in the proof, I am subtracting 10x - x.

Subtract the line above that, and tell me what you get.

[dingdongyo]

i used to be pretty good at this stuff in high school, but there were no advanced math classes in college and i rusted out. define some things for me please?

[zdunklee]

Yea, I realized that it f'd it up when I copied and pasted, see the post now for the screen shot of the proof.

[dingdongyo]

Yea, I realized that it f'd it up when I copied and pasted, see the post now for the screen shot of the proof.

ah, i've seen all those symbols before. thanks.

[Philly Mike]

WTF are you talking about???

x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

that is exactly what you wrote
you just said yourself that 9*0.999... would be 8.999...

the reason you did the statement was to show how you make it = 1 but if the math is done properly you prove that 0.999... = 0.999... and that's it.

No it doesn't in a proof you have to get the next step from the previous, I am not multiplying 9*0.999... anywhere in the proof, I am subtracting 10x - x.

Subtract the line above that, and tell me what you get.

I am not stupid, i know how to subtract. but what does the part i highlighted in red mean. last time i checked when you put a letter next to a number it means times and you put the part 9x there so it means 9 times x which is what was said.

as far as the calculus thing, I don't feel like looking into it at the moment but what it looks like (from what i understand) is just more number shuffling to try to prove the point that still makes no sense from the original number shuffling you did with the statement of
x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

[zdunklee]

No it doesn't in a proof you have to get the next step from the previous, I am not multiplying 9*0.999... anywhere in the proof, I am subtracting 10x - x.

Subtract the line above that, and tell me what you get.

I am not stupid, i know how to subtract. but what does the part i highlighted in red mean. last time i checked when you put a letter next to a number it means times and you put the part 9x there so it means 9 times x which is what was said.

as far as the calculus thing, I don't feel like looking into it at the moment but what it looks like (from what i understand) is just more number shuffling to try to prove the point that still makes no sense from the original number shuffling you did with the statement of
x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

That isn't number shuffling, it's basic math from one line to the next...

All these lines are based on definitons of operations, just like the calculus example above is based on definitons of real numbers. Like I said before there are number systems when 0.999 =! 1, but the real numbers are not one of those systems. When doing these you generally have to have a great understanding of the definitions that these systems are based upon, if you don't you aren't going to understand why it is that way.

[Howie Feltersnatch]

I blame RockMonster for this thread...

eff you dude

[Philly Mike]

9x is 9*0.999... that is supposed to equal 8.999...
in your original statement you put 9x=9
you are telling me this is not number shuffling, you posted a statement with math to show your reasoning and the math was wrong because you changed the rules of multiplication.

[zdunklee]

9x is 9*0.999... that is supposed to equal 8.999...
in your original statement you put 9x=9
you are telling me this is not number shuffling, you posted a statement with math to show your reasoning and the math was wrong because you changed the rules of multiplication.

NO I DIDN'T, I NEVER EVER MULTIPLIED TO GET THAT... how hard is that to understand, you are looking at them as seperate statements which they are not, they are equivalent statements from one line to the next.

Also, 8.999... = 9 anyway, for the same reasons that 0.999... = 1 and 0.249999... =0.25. Which is the DEFINITON OF THE REAL NUMBER SYSTEM, like I said before you need to familiarize yourself with that before you argue about it, which you are clearly not doing.

[Philly Mike]

9x is 9*0.999... that is supposed to equal 8.999...
in your original statement you put 9x=9
you are telling me this is not number shuffling, you posted a statement with math to show your reasoning and the math was wrong because you changed the rules of multiplication.

NO I DIDN'T, I NEVER EVER MULTIPLIED TO GET THAT... how hard is that to understand, you are looking at them as seperate statements which they are not, they are equivalent statements from one line to the next.

Also, 8.999... = 9 anyway.

what do you mean you never multiplied???

x = 0.9999...
10x = 9.9999... 10*0.999... =9.999...
10x - x = 9.9999... - 0.9999... 10*0.999...-0.999... = 9
9x = 9
x = 1.


those are multiplication so why is 9x any different

and 8.999... only equals 9 if you go along with the assumption that 0.999 = 1 which is what you were supposed to be showing proof of when you posted the statement itself.


The whole bases of what you are talking about with real numbers is working with the assumption that 0.999... = 1