Poll: Does 0.99 Recurring = 1

[AlphaNumeric]

Originally posted by carvegio
if you can put some what of a formal arguement together which proves 0.9r isnt equal to one. I would be happy to try and relay it to a professor at imperial and get a response if you feel the maths undergrads on this board are incapable of a proper reply

Thats what I offered about 2 dozen pages ago to AcidHell2 when he said I was wrong, and its obviously not equal, but then he said even God himself wouldn't convince him, so I doubt a Cambridge professor would...

There is always the option of posting on NRich (Haly linked to it a while back) here :
http://nrich.maths.org/discus/messages/board-topics.html
There are several PhD students who specialise in Analysis who post there who can answer these questions and points raised on a far more fundamental level than me, given they are doing their PhD's on Number Theory and Groups. Several of them are the top 1st's in their year, and dwarf even some lecturers ability-wise.

Originally posted by w11tho
And from my understanding, Alpha is about 7 months away from getting an MA in Mathematics - hardly early on in his education in Maths!

7 months from a BA, then 3 more years till it turns into an MA, whether I do a 4th year or not (one of the perks of Cambridge ), though I plan to the 4th year anyway.

 

[Harley]

Originally posted by w11tho
We will simply have to agree to disagree (i.e I say you can only look at this mathematically, you don't).

And that's why I give up. That's the closest any of the maths heads here have actually got to acknowledging the point I've been making, and all that happens is it gets dismissed. No argument, no rebuttal, just "you don't have a point 'cos it's all about maths".

I don't have a chip on my shoulder. I'm just fed up to the back teeth with people lobbing "I'll get a Field medallist to prove it to you" as if I deny the proofs. I don't, haven't and have said so a dozen times or more, starting from my very first post.

I give up because I'm sick of the overwhelming arrogance of undergraduates who think they know it all. My point is not, and NEVER HAS BEEN about the mathematical proofs. Yet all I get is the "my dad's bigger than yours" type remarks about how close someone is to an MA (and if you seriously think anyone regards "free" Oxbridge MA's seriously, stick to a career in academia, because you'll get an awakening in the real world, especially from those of us that actually worked for our Masters), or getting 'dad' to prove it to me.

I've said repeatedly that I completely defer to Alpha in maths. So what will getting a PhD student, professor or Field medallist achieve? Maybe it'll get me to defer a bit more than totally?

The sum total of the points the maths types have made about the stance I've taken is to simply dismiss the view out of hand, and repeat the mantra "it's all about maths", and to offer to repeat the proof to me. Now, apparently, not only am I not supposed to "contradict my better's" but I've got a chip on my shoulder. No argument, no discussion or debate about the fact that someone else just might have a different viewpoint, outside of a narrow speciality. Simply "it's all about maths", and when that fails, resort to condescension and insults. Jesus!

 

[Gilly]

I'm sorry it had to come to that post Harley. I admit I gave up on them a long time ago, and respect to you for carrying on trying in the face of such egotistical adversity.

It does appear that some are overwhelmed by their own immense mathematical ability (and though he wold be the one everyone think of first, I do not include George in that) and will simply not allow themselves to look at this discussion in any other way.

It is a real shame that, because we had a very interesting point that might have gone other ways had it not been put down at every turn with the simple answer 'we can explain it mathematically'.

Unfortunately at this juncture I feel the best counsel would be to give it up as a bad job.

 

[Drawoh Tesremos]

I notice that this thread has from time to time strayed away from the specific subject of whether or not 0.9r is equal to 1.

A few posts back the well known "proof" that 1 = 2 was included. That, of course was false because it included an illegal division by zero.

Here's another "proof", this time that 0 = 1. Can anyone see the flaw this time?

We'll integrate tan x, using integration by parts, and I'll use int to denote the integration symbol.

tan x = sin x / cos x = sec x sin x

So int tan x dx = int sec x sin x dx

Substitute v = sec x and du = sin x dx

Then dv = sec x tan x dx and u = - cos x


Using the integration by parts formula:
int v du = uv - int u dv

we have

int sec x sin x dx = - cos x sec x + int cos x sec x tan x dx

= - cos x / cos x + int tan x dx

= -1 + int tan x dx

We therefore have

int tan x dx = -1 + int tan x dx

so 1 = int tan x dx - int tan x dx

so 1 = 0

 

[G18241]

ok so if 0.99r IS actually 1

does that make 1.99r 2?

or do the same rules not apply to that?

 

[Harley]

Originally posted by Gilly
I'm sorry it had to come to that post Harley.

Me too. I think that's the first time I've ever posted like that, but a combination of frustration and that "chip" remark left me not inclined to just let it slide.

Originally posted by Gilly
.... I do not include George in that.....

Me neither. Alpha has shown great patience (more than I have probably) in dealing, patiently and more or less calmly, with those that refute the maths.

Originally posted by Gilly
Unfortunately at this juncture I feel the best counsel would be to give it up as a bad job.

Hint taken, Gilly )), but I'd already decided that. There's only one way I can see this will go from here if it continues, and I have no inclination to participate in that. I won't be responding any more.

 

[endeavour]

Originally posted by Drawoh Tesremos
I notice that this thread has from time to time strayed away from the specific subject of whether or not 0.9r is equal to 1.

A few posts back the well known "proof" that 1 = 2 was included. That, of course was false because it included an illegal division by zero.

Here's another "proof", this time that 0 = 1. Can anyone see the flaw this time?

We'll integrate tan x, using integration by parts, and I'll use int to denote the integration symbol.

tan x = sin x / cos x = sec x sin x

So int tan x dx = int sec x sin x dx

Substitute v = sec x and du = sin x dx

Then dv = sec x tan x dx and u = - cos x


Using the integration by parts formula:
int v du = uv - int u dv

we have

int sec x sin x dx = - cos x sec x + int cos x sec x tan x dx

= - cos x / cos x + int tan x dx

= -1 + int tan x dx

We therefore have

int tan x dx = -1 + int tan x dx

so 1 = int tan x dx - int tan x dx

so 1 = 0

Constant of integration anyone? You are trying to equate indefinite integrals.

Originally posted by g18241
ok so if 0.99r IS actually 1

does that make 1.99r 2?

or do the same rules not apply to that?

1.9r = 2, as has been stated numerous times.

 

[Ace Rimmer]

0.9r = 42

 

[Fusion]

Originally posted by Gilly
Unfortunately at this juncture I feel the best counsel would be to give it up as a bad job.

I thought the same about a week ago :/

 

[NicktheNorse]

before a full scale war breaks out is it not time to close this thread?

 

[Gilly]

Originally posted by Fusion
I thought the same about a week ago :/

At that point I still had hope that some of those that were stating the blinding obvious would possibly swing round to see that there are various ways you can approach things.

Well, those ways certainly exist, it simply appears that some are unable to accept them.

Originally posted by NicktheNorse
before a full scale war breaks out is it not time to close this thread?

Who would fight the war?

 

[w11tho]

Originally posted by Harley
The sum total of the points the maths types have made about the stance I've taken is to simply dismiss the view out of hand, and repeat the mantra "it's all about maths", and to offer to repeat the proof to me. Now, apparently, not only am I not supposed to "contradict my better's" but I've got a chip on my shoulder. No argument, no discussion or debate about the fact that someone else just might have a different viewpoint, outside of a narrow speciality. Simply "it's all about maths", and when that fails, resort to condescension and insults. Jesus!

Obviously I've got on your nerves a bit in this thread. Again I apologise - no hard feelings from my side!

 

[taliesyn]

Originally posted by Harley
I give up. I totally give up.

It isn't worth the effort.

You are quite simply wrong Harley, and clearly educationally subnormal. Just accept it

Actually, I for one agree with you (so I must be equally educationally subnormal ) that mathematically 0.9r=1 as proven, and I also agree with you that in the 'real' world, that 0.99999999...9999 ad infinitum cannot possibly be equal to 1.

Is 0.9 equal to 1? - NO
Is 0.99 equal to 1? - NO
Is 0.99999999999999999999999999999999999999999999999999999999999999999999 equal to 1? - Again, NO.

So in the *real* world, how can 1 possibly be equal to 0.9 recurring? Infinity is never reached by definition so there will always be a small difference.

I agree with the Maths collective that THEORETICALLY, 0.9r can be proven to equal 1 (for all practical purposes), but empirically it can never actually be equal.

Originally posted by Gilly
Who would fight the war?

Us and the Americans presumably

 

[Trojan]

Originally posted by taliesyn
So in the *real* world, how can 1 possibly be equal to 0.9 recurring? Infinity is never reached by definition so there will always be a small difference.

1 does indeed equal 0.9r in the real world. Look at it this way - you take a circle and split it into thirds. Three seperate pieces. Each piece is exactly 1/3 therefore each piece is exactly 0.3r. If you add the pieces together they become 1 yes?

1/3 + 1/3 +1/3 = 1

Since each third is also equal to 0.3r that means that:

0.3r + 0.3r + 0.3r = 1

But isn't the following also true?

0.3r + 0.3r + 0.3r = 0.9r

Therefore 1 = 0.9r

It exists in the real world perfectly fine. Split a cake into 3 and the 3 pieces added together equal both 1 and 0.9r ie the same value.

 

[Ex-RoNiN]

Can my vote be changed to 'Yes' from 'No', I voted before seeing the actual proof

 

[sproutpunx]

I can't join in with an adult debate without lowering myself to personal attacks and childish quips so I've had my post edited by a Don.

 

[Harley]

Originally posted by w11tho
Obviously I've got on your nerves a bit in this thread. Again I apologise - no hard feelings from my side!

Did something give me away? I thought I hid it.

No hard feelings here either, but I suspect you're dead right about one thing (in additon to the maths view of .... no, don't go there). We aren't going to agree on this.

Originally posted by taliesyn
You are quite simply wrong Harley, and clearly educationally subnormal. Just accept it

Actually, I for one agree with you ....

Cor, some people like to live dangerously. There was I, fuse lit, red glaze coming down over my vision, planning all sorts of horrible, nightmarish ends for you when ....... I got to the smiley. I admit it, for a moment, just a moment, you had me there. One-nil to you. Watch yer arse, though.

Let me guess. You were the one in the group that, as a child, thought it was a good idea to throw a banger into a wasp's nest just to "find out what will happen". It's the same mindset as "I wonder what happens if I smash two two chunks of radioactive material together extremely hard". Advice - retire to discrete distance before trying it.

 

[daz]

Originally posted by Trojan


It exists in the real world perfectly fine. Split a cake into 3 and the 3 pieces added together equal both 1 and 0.9r ie the same value.

I think this is the best explanation for it.

I think it posted it several times about 10 pages ago.

One third is exactly the same as 0.333recurring. However, 0.33 is *not* equal to one third, it is merely an approximation. 0.33333333333333333333333333333333333333 is also not equal to one third, it's an approximation. But when you use a magic calculator, that can display an infinite amount of decimal places, if you type "1 divided by 3" it will give you 0.333 recurring. If you multiply this number by 3 on the magic calculator with the infinite decimal places, you'll get 1 again. Therefore 3 * 0.3r = 1 = 0.9r ... it's hardly a mathematical proof, but it may help those of you who are struggling with the nature of infinite convergent series.

 

[Cyro]

Originally posted by Drawoh Tesremos
I don't believe I saw this answered.

1/10 has no finite decimal representation in base 3. It is a recurring decimal:

0.00220022002200...

Sorry - I'd intended that to point out that simply because there isn't a finite non-fractional representation it doesn't make the concept of the number any less definite, as AlphaNumeric did more neatly a few posts after mine.

 

[taliesyn]

Originally posted by Harley
Cor, some people like to live dangerously. There was I, fuse lit, red glaze coming down over my vision, planning all sorts of horrible, nightmarish ends for you when ....... I got to the smiley. I admit it, for a moment, just a moment, you had me there. One-nil to you. Watch yer arse, though.

Let me guess. You were the one in the group that, as a child, thought it was a good idea to throw a banger into a wasp's nest just to "find out what will happen". It's the same mindset as "I wonder what happens if I smash two two chunks of radioactive material together extremely hard". Advice - retire to discrete distance before trying it.

LOL, and I have the scars to prove it

I wouldn't actually dare disagree with you having previously read your revenge comments in the 'rape' thread ....................sir.

Originally posted by Trojan
1 does indeed equal 0.9r in the real world. Look at it this way - you take a circle and split it into thirds. Three seperate pieces. Each piece is exactly 1/3 therefore each piece is exactly 0.3r. If you add the pieces together they become 1 yes?

1/3 + 1/3 +1/3 = 1

Since each third is also equal to 0.3r that means that:

0.3r + 0.3r + 0.3r = 1

But isn't the following also true?

0.3r + 0.3r + 0.3r = 0.9r

Therefore 1 = 0.9r

It exists in the real world perfectly fine. Split a cake into 3 and the 3 pieces added together equal both 1 and 0.9r ie the same value.

So you reckon you can cut a cake exactly into thirds (down to an infinite level) in the real world do you? You must have one seriously sharp knife and a hell of a good eye

Forgive me for saying so, but that's hardly a real world example. Theoretically it can be done, but not practically which was exactly my point.