I cant belevie ppl cant put this through their heads

[pianistimo]

just joking.  you have to know that i am not a mathematician.  but, i do see the axiom , sorta.  it's been explained so many ways.  i just nod my head and say - well, if mathemticians say so -then it's probably so.  but, that doens't make it easier to stop counting pennies.  as i get older, i simply don't like it that things are not itemized.  the more 'things' involved - the less precise.  i like things not to be lumped together - so to speak - but to be exactly itemized.  this is not the axiom thinking.  to me, axiom and philosophy kinda go together.  you say - if this is true - then this also could be true.  but who knows if the first thing was true.  what if you said you had 12 chocolate donuts make up of a practically infinate number of wheat particles ground into flour.   the chaff was not counted because before the donuts were made - that was eliminated.  then, the flour was processed and anything resembling roughage was also eliminated.  the remaining flour was made of soft flour particles that looked like more than they were because of fluffing.  but, when water was poured over it - it's residual nature was the size of a dime.   (farming communities in pennsylvania have made me think deeply about organic food).   - ok.  so the label on the donuts says such and such amount of carbohydrates - which could be an infinate number of small flecks of flour but it's put into a number.  a hypothetical number.  because we know that all foods have to have numbers on them (percentages of this and that).  but, when it's actually measured - we find that the real amount has been changed by .009%  and incrementally every year there is .09 and then .9 percent that is taken out of the flour and it is whipped with self rising stuff so that the rising materials make up for the lack of flour.  only in 20 years are the box sizes changed.

[prometheus]

It has nothing to do with counting or any everyday use of numbers.

To 'solve' the problem you either need to ban the use of infinite 9's or you need to make .999~ smaller than 1.

If you do the first then you have a problem. Infinity minus 1 is still infinity. Take a very big number and you can still add 1 and not reach infinity. So defining a maximum number of decimals is impossible.

This means you need to create a different system. Since I am also not a mathematician I don't know how to create a good one. The only thing I can come up with is that 1 minus .999~ equals .1, so that .999~ and 1 are not the same number. The difference is .1. This means that in that system .999~ equals our 1 and their 1 equals our 1.1. In this system it is not possible to express numbers like our 1.001 and 1.09. The interval (1,1.1) does not exist and cannot be used.

Now you can do it differently, decreasing the result of 1 minus .999~ in that system, to for example .01. But then you can't express numbers like 1.001 and 1.009. And no matter how small you make the difference between 1 and .999~, the problem remains. It just becomes smaller. Now you can make the difference between the two infinitesmall and solve the problem. But that is exactly how it is now. And that is the solution you claim to be idiotic.


So this system is idiotic since it is not able to express all numbers.

I am sure a mathematician could up with a 'real' alternative, changing something much deeper. But until you know of such a system don't claim this one is idiotic. This is because the basic 'problem' is one that cannot be solved that easy. This problem of not being allowed to use infinitely long numbers while at the same time not getting any other problems doesn't seem to be directly solveble.


And what is the cause of this 'problem'? It is not being able to accept a system where .999~ equals 1. But is that really so much of a problem?

[pianistimo]

there is no precision with infinity anyway - so why try.  it's like a scientist telling you there are a certain number of stars in a galaxy.  who really cares and is going to remember those.  you have to refer to the article each time you want to know the number.  and, basically, they are guessing (like with jars asking 'how many jelly beans')  we don't know if there is a round rubber ball in the center with the jelly beans all around it.  face it.  scientists will never know it all until God tells us.  but, that doesn't stop us from trying.  if i knew upper level math - i'd probably play around with infinity and enjoy the concepts.  it frustrates me at this point.

[prometheus]

I don't understand your point or problem. I see no relevance to astronomy.

Infinity doesn't really care about accuracy. As for a system that allows infinite numbers or numbers with infinite decimals, it seems accurate enough. If the current system isn't accurate enough for you then propose something else.

Up to now this number systen has been found effective enough to let us be able to make the complex calculations needed to build computers, which allow us to communicate right now. Don't underestimate the complex theories that are the basis for this everyday technology.


I guess it is pretty natural to be frustrated by something you cannot understand. I am not sure if this is the reason or not, but it could be one. A position of ignorance puts you in the position where you just have to accept that what the 'high brow scientists' claim.

[pianistimo]

there's no doubt that advanced math is very important to our civilization.  i'm just saying - if it's not practical in everyday life - i am not that interested.  let the scientists here figure it out.  if i told you that God knows every hair on your head (without counting probably) you would be amazed, too.  you'd probably say ' well, what about the ones that are falling out and the ones that are just starting to grow in.'  again,  conundrum.  will we ever know.  i say, if you really want the answer to a question - ask God.  even some scientists do this before they start their experiments and procedures.  being guided on a very small Y turn can keep you from going down a path of which there is a much different answer.  of course, there are a limited number of people who are going to check your answers.   maybe stephen hawking.  i heard that it was one or two people that came up with the invention of the computer (and not a room full).   

[bflatminor24]

there's no doubt that advanced math is very important to our civilization.  i'm just saying - if it's not practical in everyday life - i am not that interested.  let the scientists here figure it out.  if i told you that God knows every hair on your head (without counting probably) you would be amazed, too.  you'd probably say ' well, what about the ones that are falling out and the ones that are just starting to grow in.'  again,  conundrum.  will we ever know.  i say, if you really want the answer to a question - ask God.  even some scientists do this before they start their experiments and procedures.  being guided on a very small Y turn can keep you from going down a path of which there is a much different answer.  of course, there are a limited number of people who are going to check your answers.   maybe stephen hawking.  i heard that it was one or two people that came up with the invention of the computer (and not a room full).   

Can't you ever stay on one topic? I swear - your digressions plus your poor spelling and grammar make your posts a headache.

What does this have to do with God?

If you "aren't that interested" and we should just "leave it to the scientists" then why are you pontificating about a subject you know very little about?

That goes for all of the rest of you, too. If you don't get it, just accept it and move on. Don't waste people's time.

.9bar = 1.

~Max~

[pianistimo]

well, mr., if you think this is an important topic - tell me what you do with it.

[prometheus]

If a scientists already know what the outcome of a experiment ought to be, either through god or some other delusion and it actually does happen quite often, then this is bad because it can influence the accuracy of the experiment or the interpretation of the data.

[prometheus]

well, mr., if you think this is an important topic - tell me what you do with it.

Tell someone how many years ago we were born. Tell someone how many breads we want when we buy food. And understand how much money we need to pay for that. Things like that.

Now, don't go around and claim you don't use money...

[pianistimo]

that's exactly what i'm saying.  we use money.  the increments don't go below two digits past the decimal.

but,  you and bflatminor can continue to argue this until the moon turns blue.

[prometheus]

So? Maybe you should look a closer look at what I said. I said I use the number system for those things. Part of this number system is that 1 equals .999~

You do the same thing. There is no way around. I mean, you can choose to ignore the implications and characteristics of your number system and never go beyong using integers for both euro's and cents (or dollars). But that doesn't mean those things do not exist.

[pianistimo]

but what ARE the implications?  if you can't really prove them to the average person, you are talking among yourselves. 

honestly, i am awed by scientists and mathematicians.  but, they've never been known for cleaning up after themselves.  look at what happens to their desks. 

i'd say there's room in the world for those that are very smart and those that are pragmatic.  the pragmatic ones win because they help the very smart ones find their stuff.

[prometheus]

For one that .999~ equals 1.


If this is not true then it needs to be explained in the way I decribed before.



I wonder if you can imagine imaginary numbers. These numbers are so odd that you can't even write them down correctly with our number system. The square of these numbers are negative. So what are these numbers themselves? Thats something to thing about. I mean, everyone knows that you can't take the square of a negative number.

An example of an imaginary number is i^2 + 1 = 0 where i is the imaginary number.

Do you know that some people oppose the existence of negative numnbers because they claim them to be fictitious and useless? This includes Descartes.

But does zero exist? Shouldn't we stop using it? I mean, have you ever been to the baker to buy zero breads? Probably not.

Are there days where you bought exactly zero breads? Yes, of course. So how does this work? Huh?

[pianistimo]

i agree with descartes.  in real life - a penny broken into infinity is dust.  therefore, useless.

but if you and bflatminor come up with some really great inventions using the infinity process - then you might be the first to discover WHY an imaginary number squared is negative. 

these things truly are puzzling.  and, when you find a good possible answer - it's probably going to help something somewhere in the world.  say the world of microbes or viruses?  i don't know.  my neighbor is really smart.  she hardly ever talks.  i go over and do all the talking.  and she nods and smiles.  she uses me.

[berrt]

you might be the first to discover WHY an imaginary number squared is negative. 

because it's defined to be so. that ends ANY discussion   

b.

[counterpoint]

Really funny discussion in this thread 

I hope, nobody will dispute, that you can divide a line of 1 m in 3 equal parts. Each part is 1/3 m long. If you calculate the division into the decimal system, you will get 0.33333 (and  there will always be a tiny little rest, which forces you to add some more 3s to the number)
The only problem is, that when calculating 1/3 with a computer, it will only have a limited number of digits. So the result will be wrong on any computer. Perhaps that's the reason, why people don't accept the existence of periodical decimals. Because for a  computer, something like periodical decimals could not exist .

But in a human brain, periodical decimals can exist.

Not in all human brains, but in some they can and they do 

[pianistimo]

to what degree?

[counterpoint]

to what degree?

1 out of 3 ? 

[prometheus]

Well, the whole issue is what it means for a number 'to exist'.

Imaginary numbers don't exist in the same sense as one and two exist. But surely they can defined and used without any problem, except for the fact that they are ' odd', whatever that means.

[pianistimo]

i am still stutterring over why an imaginary number squared is negative.  now a positive whole number squared is not unless there is a negative sign in front of the number.

say, did you know that in the ny times fashion editorials - eyebrows are 'in' again.  instead of a finite number of well groomed hairs - women (and probably men) are supposed to just let them grow wildly back.  putting a little clear mascara on them to make them have some windswept features. 

now, as i see it - math has fashions.  one year - infinite numbers are in.  the next year, no one talks about them.  is this correct?  seems that music teachers do the same thing.  one year there's this all important textbook.  the next year - it's old hat and have to find something different.  they all cost $65. dollars.  who's making the money?

[counterpoint]

i am still stutterring over why an imaginary number squared is negative. 

I am wondering much more, why multiplying two negative numbers give a positive result   

it's mathematics, not everyday logic

[pianistimo]

maybe it all get's down to electricity.  everything has a positive and negative charge.  too much on one side and it's lopsided and loses magnetism or something.  maybe there has to be an exactly equal number of positive and negative numbers.  do you think?

[counterpoint]

If you ask me

it is okay to multiply a negative number and a positive number

but I would not allow multiplying two negative numbers.

[pianistimo]

anions and cations  (negative charged ions and positve charged ions). 

now if we put two anions together, they'd just keep pushing apart, right?  but if you put two cations together, what happens?  you produce millions of neutrons.

[counterpoint]

but if you put two cations together, what happens?  you produce millions of neutrons.

Really? I never tried this... 

[pianistimo]

yes.  this proves my theory that nothing and zero are very easy to make.  but, infinity is very difficult.  (actually, i'm just making this up as i go).  but, i did read the last post and am now studying 'axioms for real numbers.'

[leahcim]

that .999... and 1 are the same number.

I just spent 10 minutes areguin with someone -_- , and the things he said...

I'd forget the 0.3333 * 3 and similar tricks.

Grab an analysis book. i.e one of those undergrad texts.

Show 'em the axioms / proofs [which are relatively straightforward as proofs go. You perhaps know them already?]

For starters :-
(a) axioms of the real numbers and
(b) proof that between any 2 rational numbers there's an irrational and
(c) proof that between any 2 irrational numbers there's a rational.

Ergo, in order for 0.999 recurring to differ from 1 then (a), (b) and (c) above must yield some irrational and rational numbers that you can prove must exist between them, for them to be different [or else you'll have a contradiction that they are different and they must be the same]

Or, a similar idea - ask them to answer "what the smallest real number less than 1 [or greater than zero]?" If it is [according to them] 0.999 recurring or 0.000000000 <infinity more zeros> 1, then again, the proofs that there are as many rationals and irrationals as you want between rationals and irrationals will reach inconsistencies they can't address by their choice of this number.

You'll have moved the problem beyond the learning of most who haven't read the first few chapters of an analysis book.

Anything else, in a sense would be like arguing with a toddler than 5 - 10 = 'can't do it' and you are saying "oh yes you can it's -5'. You probably wouldn't bother, no? If they are genuinely interested in maths, they'll lap up those early proofs and the stuff in that analysis book, because although it's what most of us take for granted in primary school days when we did arithmatic, the penny drops on a lot of maths we learn at school without been given formal proofs when we see those proofs.

But maths that is already proven is just there for anyone to read and learn by rote if we want. If it's not a new proof, what's to argue or debate about it?

Unless you want to "prove" that you have a better memory or a bigger willy or something, the only real thing that matters about maths in itself, is coming up with something new.

[The alternative, of course, is using the maths for some purpose, building a bridge, a computer or whatever] but 0.999 recurring being the same as 1 was inconclusively proven before anyone who wants to argue about it today was born. How can you argue about it? It's not like "Is there a God?" or "What is the best operating system?" Show them the proof, if they don't accept that, they don't accept maths as true.

OTOH, knowing it's true is largely a trivial bit of knowledge relative to discovering it - e.g the fact that I might know pi is transcendental is easy to know now, the proof itself although slightly harder to learn is still trivial to repeat. Truely understanding the proof isn't trivial, but is nevertheless a fairly useless exercise if that's as a means of debating with someone who might not know that it's true - [especially if that's the wag who is going to decide that in base PI it's an integer]

[pianistimo]

multiplicative identity (proves uniqueness?)  now 0 doesn't equal 1  but how does that relate to a number such as x = 1   ?

oh yes!  it all gets back to that guy who invented dedekind cuts.  dedekind himself.

so actually, if i wanted, i could say .9999~ is less than OR equal to 1.  but dedekind cut it.

[pianistimo]

how can one man have so much power over numbers? 

now, matrices.  what's the thing with those?  i mean those are very random and arbitrary too.  it's like saying that because most things are true- that everything in them is true.  what if they aren't.  what if they are random?  what if upper math is entirely random.

take this one for instance:

    3            1 0 0
X        =      0 1 0
                   0 0 1

now what's this about MAPLE?  apparrently it does machine rounding.  but someone found errors in it.  you see!  computers are illogical.  some kid used the program thinking he'd get an A, but the teacher marked one of his answers wrong.

www.maplesoft.com/products/MSK/MSKToc.html

[bflatminor24]

i am still stutterring over why an imaginary number squared is negative.  now a positive whole number squared is not unless there is a negative sign in front of the number.

say, did you know that in the ny times fashion editorials - eyebrows are 'in' again.  instead of a finite number of well groomed hairs - women (and probably men) are supposed to just let them grow wildly back.  putting a little clear mascara on them to make them have some windswept features. 

now, as i see it - math has fashions.  one year - infinite numbers are in.  the next year, no one talks about them.  is this correct?  seems that music teachers do the same thing.  one year there's this all important textbook.  the next year - it's old hat and have to find something different.  they all cost $65. dollars.  who's making the money?

What the hell are you talking about? You must have adult ADHD or something because I can't follow any of your logic or trains of thought. Eyebrows are "in?" Math has "fashions?" Who is making money from new textbooks? What the hell...

I still can't figure out what this whole thread is even about. Nobody has written anything interesting or worthwhile. Time to change topics.

[steveie986]

I think pianistimo is a comedic genius. Those who take her seriously and actually try to argue with her simply can't appreciate her wit.

[jre58591]

this thread is pointless. close it please. we are all getting nowhere. we are only arguing pointlessly over something so trivial.

[leahcim]

I think pianistimo is a comedic genius.

I think proof by little britain sketch works here

<man approaches garage / car boot sale>
Man : "Hello, how much are the Red Dwarf videos?"
Hypnotist "£10"
Man : "Nooo, too much..."
Hypnotist "Look into my eyes, look into my eyes, 1, 2, 3 you love red dwarf you'll
pay £10 for the videos, 1, 2, 3 wake up and remember nothing..."
Man : "I love Red Dwarf here's £10..."
Man : "Is that the brotherhood of man?"
Hypnotist : "Yes sir...look into my eyes look into my eyes, 1, 2, 3 you love the Brotherhood of man, you want to buy their CD"
Man : "I love the BoM, I would like to buy their CD..."
Hypnotist : "Thank you sir, would you like this Piantisimo DVD, it's hilarious"
Man : "Nah, she's not funny..."
Hypnotist : "Look into my eyes, look into my eyes, 1, 2, 3 you're asleep. Pianistimo's DVD is very funny and you want to buy it"
Man : "Now you're pushing your luck Mate"

[kony]

i^2 + 1 is not an Imaginary number. an Imaginary number only consists of a certain amount of i (a linear amount of i, i.e. no powers on i). if it has anything more than that, it's not Imaginary, it's Complex.

but Complex numbers have nothing to do with this.

[maul]

... so basically never listen to anything prometheus says. Ever.

[johnny-boy]

... so basically never listen to anything prometheus says. Ever.

 

[nicco]

Well, i asked a friend of mine this and he told me 1 and 0.999... is not the same.

I confronted him with the following "proof":

x = .999bar
10x = 9.999bar
10x – x = 9x, which is the same as 9.999bar - .999bar, which is 9.
9x = 9
x = 1

And he gave me the following correction:

x = 1 - dx bar
10x = 10 - 10dx bar
10x - x = 9x, which is the same as (10 - 10dx) bar - (1 - 1dx) bar, which is (9 - 9dx) bar
9x = 9 - 9dx
x = 1 - 1dx

where dx is infinitely small.

He did say that this is something a normal math student wouldnt understand, you need something more than just basic knowledge. The above is the correct way to express it.

He would also like to recommend this book for those of you who want to understand:

https://www.amazon.com/gp/product/0312185480/sr=8-1/qid=1155945317/ref=pd_bbs_1/103-0714617-3797437?ie=UTF8

[prometheus]

i^2 + 1 is not an Imaginary number. an Imaginary number only consists of a certain amount of i (a linear amount of i, i.e. no powers on i). if it has anything more than that, it's not Imaginary, it's Complex.

but Complex numbers have nothing to do with this.

I was talking to Pianistimo. What do you think would have happened when I also added the 'a + bi'-part?

[prometheus]

... so basically never listen to anything prometheus says. Ever.

I had to click on your history to see who you are. Apprently all your posts are insults, of the most shallow kind, aimed at me.

Everyone, just look here and have a good laught: https://www.pianostreet.com/smf/index.php?action=profile;u=5238;sa=showPosts


This guy must be somones clone used to launch low-quality insults at me. So who is he really?

[prometheus]

Well, i asked a friend of mine this and he told me 1 and 0.999... is not the same.

[...]

I am sorry to say but I think he was just making fun out of you

He uses dx which means differential. It is not a number and can only be used in special cases as if they were numbers. For example dy/dx, to express the derivative.

If you do want to try to understand what is expressed you can only understand dx as being equal to zero. Which would result in:

x = 1
10x = 10
10x - x = 9x
9x = 9
x = 1

I mean, that doesn't go anywhere.

Furtermore, you can't prove that 1 equals .999~ or not because this has only to do with axioms, assuptions. They equal each other by definition. The axiom is the basis on which you can prove other things.

Also, every math student gets calculus. That is the whole point of studying math.

[pianistimo]

i understood it better when nicco said dx meant infinitely small.  then it was just an algebraic equation.

[prometheus]

But dx isn't just infinitesmall: https://en.wikipedia.org/wiki/Differential_%28calculus%29


It is not a number of constant. It is not part of algabra, since the link to a calculus book.


I don't really understand what his friend meant with 'dx bar' and what the difference is between 'x = 1 - dx bar' and 'x = 1 - 1dx'. Both would mean: 'x = 1 - 0'

I don't see any reference to .999~

[pianistimo]

it's not a number of constant?  so it does get infinitely smaller?  then, that proves that it cannot be equal to one.  and yet...it gets so close.  but when multiplied by 10 and then subtracted becomes 8.9999 and 7.99999 and 6.99999.  so we see that someone is robbing peter to pay paul.

[prometheus]

No, it is not a number. It cannot be used to calculate. It is a 'trick' used in calculus to get the derivative, which gives the slope, of a function.

To calculate a slope you can use Δy/Δx. There the slope over the area as big as Δ is given. But when we want to calculate the slope in a particular point, not a particilar area, we need to have a Δ that is as small as possible. And that is what dy/dx is.

You can use the infinite small in this case because both the numerator and the denominator have this concept. The effect is that you get a perfect result because the smaller delta is, the more accurate the result. So when it is infinite small it is as accurate as possible.

But it is not an actual number, it has no value. You cannot multiply it with 10. You cannot subtract anything from it.


So like the wiki page describes:

This is a consequence of the slope equation m = Δy/Δx where the only difference is the replacement of Deltas with differentials to reflect the fact that the x and y values are at one point, not across two.

Also, why did you think that dx times 10 is 9.99~ ?

[leahcim]

Well, i asked a friend of mine this and he told me 1 and 0.999... is not the same.

I confronted him with the following "proof":

0.9999bar is a rational number. That means it can be expressed at the ratio of
2 integers a and b. So there's no real need to talk about infinitely small anything, no more than there is for 1/9, 2/9, 3/9 (or 1/3), 4/9, 5/9.... and so on until you get to 9/9 which is equal to 0.9999 recurring.

e.g

1/9 = 0.111111111 rec
2/9 = 0.222222222 rec
...
8/9 = 0.888888888 rec

At which point 9/9 should be pretty clearly 0.9999999 rec if you want to do maths by observation [which is where I suppose 0.9999 'looking' smaller comes from]

To believe it isn't must require a lot of handwaving about crumbs accounting for the missing bits if you are cutting a cake into 9 pieces

According to your friend, if you cut something into 9 equal pieces the 9th piece is magically bigger than the rest so that you can go from 8/9 to 1 when you add them. Worth a physics paper or 3 "On the electrodynamics of a hot body, like a piece of birthday cake, expanding in the direction of travel through the ether at velocity near c...Method : During Prof Morley's birthday we cut his cake into 9 equal pieces and threw him out of the lab window to test the local gravity, next we... (cont pg 72)"

Suppose it is, swap it with one of the others [this may cause arguments amongst siblings] and add them one by one.

Now you have 2 pieces such that 1/9 + 1/9 > 2/9.  Remarkable book that must be

OTOH, if you want proofs without quotes around them

The proof that for x,y real numbers with x < y there exists a rational r, such than x < r < y, from which you should be able to find r if 9/9 isn't equal to 1.

Similary, since both are rationals the proof that between any 2 distinct rational numbers there exists an irrational [e.g for p/q and m/n, with m/n < p/q] the number

(m/n) + sqrt(2)/2 (p/q - m/n) lies between them.

Again for m/n = 9/9 and p/q = 1 there's a contradiction suggesting they are the same.

Either you don't accept 0.999999 rec = 9/9, but since it's clearly rational, what is it as a / b? If it were irrational, the idea that some rationals, a/b were closer and closer to it, would make sense, indeed you can get as close as you want. But all rational with infinite decimal expansions [0.xxxx rec or 0.abcabcabc and so on] don't have that problem, they are exactly equal to said ratio, why would 9/9 be any different?

[counterpoint]

waiting for the "snap"

supposed, we have an endless stripe of paper
at the beginning we write 0.9
then we add one 9 after the other, perhaps one at a second
we can do this for a week... for a year ...  for hundred years (changing the writing person of course) ... for millions of years

the digits at the beginning of the stripe will always be 0.9
they never will change to 1.0

perhaps thats the reason, why it is so hard to believe, that the value of the number will be 1 when it comes to infinity...

[leahcim]

perhaps thats the reason, why it is so hard to believe, that the value of the number will be 1 when it comes to infinity...

Yes, but I think it's confusing properties of the irrationals with rationals.

e.g pi is equal to pi. It's the ratio between the circum and diam. of a circle.

If you were to say what is pi = a/b? Then you can't. You can get as close as dammit, but not equal.

Similary, if you say

3 < pi
3.1 < pi
3.14 < pi

and so on, you get as close as you like, but never there.

OTOH.

0.1111 rec equals 1/9. You're there already, there's no closer to get. Nothing you can add to get closer, no number you can express that is between them. Even though you can say


0.1 < 1/9 and
0.11 < 1/9

0.111 rec is there.

Similary, 0.999 rec is already one, you can't get closer [whereas you can trivially get closer if you have 0.999 or 0.9999999999 or 0.999<10 billion billion billion 9's>], it doesn't need to change into 1.

OTOH if you have a problem than 0.999 looks different, say

"one equals naught point nine nine recurring"

Translate that into 200 languages. Most of which you won't understand. Write the expression in multiple bases. Find alien life and see how they write the expression.

All of which may help lose that we're "taught" to do maths for years and years before we're taught the stuff behind it [indeed most of us don't get that far - plenty will tell you pi is 22/7 because of that]

i.e If it's the representation that's confusing, change it, but note that the proofs behind maths don't rely on the representation.

You're doing nothing different when you say 1/9 * 9 = 1. Except that when we learn how to do sums with fractions when we're primary school kids [well, it's probably A level stuff these days ] , we get a few tricks that perhaps make it easier to accept on face value that 9/9 = 1. But if you can accept the fraction then any, even philosophical sense, that you might feel 0.9999999999 rec isn't quite the same as 1 is in that fraction too.

e.g an axiom says that there's a rational number such that if you multiply it by 3 you get 1. 1/3 is a symbol for that number, so is 0.3333333 rec.

The other issue is that of what you can draw or write on bits of paper. Maths is abstract. Circles, rectangles and stuff like that don't actually exist, you can't draw them, does that mean you struggle to accept that a rectangle can have a specific area?

What about a piece of A4 paper? It isn't actually a rectangle. Similar a number like "4.24" you might be able to write on that piece of paper, but that's no better or worse a symbol than pi or 0.9999 rec, simply because it has some kind of finite length in one number system.

It has only very limited relationship with anything you can actually physically make or manipulate. 9/9 will never change into 1 either, unless you've very special paper.

Nevertheless there's a definite sense in which maths works [I can get my glass to fit in the frames when I treat them like rectangles] So I would say, in the abstract sense maths has things that are equal to other things [as well as close approximations and isomorphism and all that other jazz] but whenever you try to take even the most simple finite maths and say "I can do this on a piece of paper..." you'll be struggling to have anything that is exact or equal - I don't think you need an infinity of 9s to get to that issue though.

Or another way, say you and 2 friends did some work on my house and I said I'll split £369 quid with you, 1/3 each..keeping it nice and straightforward so we don't have to argue over splitting £1. You're happy that you get £123 each.

Then on the day I give you 0.33333 rec each and you each take the £123 but one of you says "Eh, I know a bit of maths, he's only given us 0.9999 rec, he's kept some of the money" and you beat me up for the rest of it. When the other one says "Hang on, we've got £369 between us and £123 each, his pockets are empty....." and the 3rd guy says "Ah! I asked my friend, he says it's because he only kept a very tiny amount" Principles being what they are you all beat each other up until the police arrive arguing over which pile of £123 had the tiny amount less

[lau]

I'm gonna give you the benefit of the doubt and assume you're joking.

However if you aren't, show me a mathematical proof that they are different, and I will show you 5 or 6 that they are the exact same.

i'm going to give YOU the benifit of the doubt and assume you are telling me something hilariously not funny.

(I can't believe ppl can't put this through their heads)

if x= .99999ect...  and  y= 1 , then  x equals point nine freaking nine and y equals 1.         

[leahcim]

if x= .99999ect...then  x equals point nine freaking nine

I think you're arguing with yourself there

[lau]

how am i arguing with myself?  Maybe it's because i said the numbers in word form.

is said "freaking .99" not freaking 9.9

best wishes that won't flipping come true anyway, Lau