Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**Toast****Real Member**- Registered: 2006-10-08
- Posts: 1,321

Comprehensible or Comprehendible might do the trick

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,529

It is in the Urban Dictionary: http://www.urbandictionary.com/define.php?term=comprehendable

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

yes, and comprehend**i**ble is the proper english word

*Last edited by luca-deltodesco (2007-01-26 11:18:00)*

The Beginning Of All Things To End.

The End Of All Things To Come.

Offline

**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

To Ricky!

Quote:

"ARB, your request for proofs has been met. We have provided many. You, to what I have seen, have yet to make a comprehendable objection to these proofs."

ARB

Gather together all the Examples into One Example! that you think are a Counter Proof! and I will Answer! from my Side I have seen Nothing So Far! Only People putting forward So called Counter Proofs! that are using Numbers Nothing to do with what I have put at the Start of this Post!

It's Quite Simple use the Variables/Numbers A,B, & C and give me what you are Made of! so far in other Arguments we have had! I am well ahead of you!! and you know it! FLT etc.....

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

ARB, you have been weighed, you have been measured, and you have been found wanting. We have done so before, and to think doing the same again will result in a different outcome is the definition of insanity. I will not waste any more time on this "problem" until an objection that actually makes sense is made. I consider it solved until the time being, and I have no interest in solving it further.

As for comprehendable, Google doesn't give me any suggestions on how to spell it, even though it's one letter off. I declare shenanigans!

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,529

Is this dible-dable quibble?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

Comprehendible FTW.

Offline

**Toast****Real Member**- Registered: 2006-10-08
- Posts: 1,321

Funny that. I've always used comprehensible in my studies.

Offline

**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

OK!

Below is Needed because No One! is prepared to put forward an Example,in a line by line way! the same as my Proof! to explain what they are trying to say!

The main problems are not saying at what stage A & B are at! i.e Single Start Values! or Calculated x C.

I am going to Add some new Variables so everyone knows what is Happening!

Sometimes new Variables have to be Add to explain things in an easier way,a good example is the N2 = Infinite 0.9999..."is it possible to insert anymore Numbers Between! " N3 = 1

as soon as I introduced the N4 Variable = The Maximum possible Number of .9's ?

Everyone was stumped! Because as they know as soon as anyone gives a Value for N4,I will answer with N2..............(.N4 + "as many more .9s I want to Insert!.)...........N3.

----------------------------------------------------------------------------------------------------------------

INFINITE 0.9 <> 1 PROOF By,Anthony.R.Brown,29/01/07.

The Variables below A1 & B1 are Both Single Start Values.

A1 = 1 "This has to be the Start Value for 1"

B1 = 0.9 "This has to be the Start Value for Infinite 0.9"

C = A1 / B1 = 1.1111111111...."There is only one Value & Variable for C"

A2 = A1 x C = 1.1111111111 ......"This is the same single Calculation as B2"

B2 = B1 x C = 0.9999999999 ......"This is now Infinite 0.9 and a single Calculation"

If B1 or B2 was at anytime to = A1 Then either would end up with the same Result as A2,but because it will take more than one single Calculation! for B1 or B2 to = A1

Then its Impossible from the Start for Infinite 0.9 to ever = 1 in a single Calculation.

Offline

**Dross****Member**- Registered: 2006-08-24
- Posts: 325

As you like it, Anthony...

A1 = 1

B1 = 0.9

**C = A1 / B1 = 1 / 0.9 = 1.1111...**

**B2= B1 x C = 0.9 x 1.1111... = 0.9999...**

These are all as you previously defined them. Now watch:

0.9999... = B2

= B1 x C

= B1 x (A1 / B1)

= (B1 / B1) x A1

= 1 x A1

= A1

= 1

This demonstrates that 0.9999... = 1. Are there any objections to what is above? Are there any flaws in there? I would like to see them if there are.

*Last edited by Dross (2007-01-29 02:16:24)*

Bad speling makes me [sic]

Offline

**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

QUOTE:

0.9999... = B2

= B1 x C

= B1 x (A1 / B1)

= (B1 / B1) x A1

= 1 x A1

= A1

= 1

A.R.B

All that is happening in the above Calculation! is! Infinite 0.9 is being Made to = 1 by Adding the Difference of 0.1 in a round about way!

It's the same as me Saying N1 = 5 N2 = 4 "Now make N2 = N1" N3 = N1 / N1

Result = N2 = N3 x N1

Now Below..........................................................................................................................

A2 = A1 x C = 1.1111111111 ......

B2 = B1 x C = 0.9999999999 ......

In the above Single Calculation! Because A1 is 1 it Ends up with a Value A2 > B1 or B2

B2 = B1 x C = 0.9999999999 ....B2 is Now Infinite 0.999..This takes One Calculation!

The above Proves!! if Infinite 0.9 was Equal to 1 it would by a Single Calculation! End up with the same Value as A1 x C

Offline

**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

Anthony.R.Brown wrote:

It's the same as me Saying N1 = 5 N2 = 4 "Now make N2 = N1" N3 = N1 / N1

Result = N2 = N3 x N1

I'm sorry, but 5 times 1 doesn't equal 4.... N3 is going to be 1 since 5/5 is 1, and N1 is still 5, so N3 times N1 is 5. N2 was 4 so N3 times N1 != N2

The rest made no sense

Support MathsIsFun.com by clicking on the banners.

What music do I listen to? Clicky click

Offline

**Dross****Member**- Registered: 2006-08-24
- Posts: 325

Anthony.R.Brown wrote:

Dross wrote:0.9999... = B2

= B1 x C

= B1 x (A1 / B1)

= (B1 / B1) x A1

= 1 x A1

= A1

= 1All that is happening in the above Calculation! is! Infinite 0.9 is being Made to = 1 by Adding the Difference of 0.1 in a round about way!

And at what stage in the above calculation is that happening, exactly?

What I have posted is an equality between 0.9999... and 1 - nothing is added, nothing is taken away and most importantly *nothing is changed*. All that is happening is that something is revealed.

The first step is true by our definition of B2.

The second step also true because of this definition.

The third step is true by our definition of C.

The fourth step is true because of the associativity of the real numbers.

The fifth step is true because whenever we divide a non-zero element by itself, we get the identity element - in this case 1.

The sixth step is true because multiplying an element by the identity element doesn't change the original element*.

The seventh step is true because of our definition of A1.

So, where *exactly* is the flaw in the logic? If you point one out (please don't be vague - give the *specific* step, it has to happen somewhere) then I will admit that it is wrong - I've always been big enough to admit when I'm wrong.

Otherwise, you have the counter-proof you requested staring you in the face, and you still cannot admit that 0.9999... = 1.

To stress the point - nowhere in the above does it say "0.9999... + <something> = 1". All it says, is "0.9999... = <something> = ... = 1. It's an identity between 0.9999... and 1, and none of the values used inbetween change at all.

* - see? *No change!*

Bad speling makes me [sic]

Offline

**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

no anthony, he has done no such thing as what you suggested, he has used youre own equations, and shown you how they can be rearranged without changing any corresponding values, to give 1.

/*quote*/

NFINITE 0.9 <> 1 PROOF By,Anthony.R.Brown,29/01/07.

**The Variables below A1 & B1 are Both Single Start Values.**

**A1 = 1 "This has to be the Start Value for 1"**

**B1 = 0.9 "This has to be the Start Value for Infinite 0.9"**

C = A1 / B1 = 1.1111111111...."There is only one Value & Variable for C"

A2 = A1 x C = 1.1111111111 ......"This is the same single Calculation as B2"

B2 = B1 x C = 0.9999999999 ......"This is now Infinite 0.9 and a single Calculation"

**If B1 or B2 was at anytime to = A1 Then either would end up with the same Result as A2,but because it will take more than one single Calculation! for B1 or B2 to = A1Then its Impossible from the Start for Infinite 0.9 to ever = 1 in a single Calculation.**

/*quote*/

OK, lets take this easy,

you state, simply:

a[sub]1[/sub] = 1

b[sub]1[/sub] = 0.9

**c = a[sub]1[/sub] / b[sub]1[/sub] = 1.111...,** this is perfectly true.**a[sub]2[/sub] = a[sub]1[/sub]c = 1.111....**

now, lets substitute some of your own variables

*a[sub]2[/sub] = a[sub]1[/sub]c = 1.111....c = a[sub]1[/sub] / b[sub]1[/sub]*

therefore:

since

so:

this is all in line with what you have said, that a[sub]2[/sub] = c = 1.111...

now you get youre last line, which is:

** b[sub]2[/sub] = b[sub]1[/sub] x c = 0.999... **

now, you have, already established that ** c = a[sub]1[/sub]/b[sub]1[/sub] **

therefore:

* b[sub]2[/sub] = b[sub]1[/sub] × c = 0.999.... = b[sub]1[/sub] × a[sub]1[/sub]/b[sub]1[/sub] = a[sub]1[/sub] = 1 *

therefore: using you exact equations, and values, without changing anything, without adding anything, without removing anything, i have shown that 0.999.... and 1 are the same.

please identify where you think i am going against what you have used.

The Beginning Of All Things To End.

The End Of All Things To Come.

Offline

**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

NOW I WILL SILENCE EVERYONE!

-------------------------------------------------------------------------------------------------------------------------------------

I have been waiting to Post the following Post for some time Now! I can wait any Longer!!

Maybe I was hoping someone would put forward Something Amazing! But Deep down I always knew my Proof would stand the test of Time!

A1 - 01 "A1 now equals 0.9" "I am going to put the remaining 0.1 on the side,and come back to it later!"

A1 x C "This now equals Infinite 0.999.." "Hands up everyone who thinks this will now equal 1" " yes that,s you! and you! and every other person who doubts this Proof!"

Now I will do something! that an Accountant would be proud of! (if it was allowed)

A1 + "The 0.1 I put on the side at the beginning "

Some how The original A1 = 1 has become 1.1 and yet at no time was 0.1 ever Add to A1

Can you imagine every Money Investment House doing this to every 0.9 they find within their Customers Accounts!

Someone would be making an Enormous amount of Money!!

But Unfortunately for the Investment Houses it would be illegal! Because the Math don't Add up! "You cant turn a Number that starts as 0.9 into 1 without someone Noticing!

Offline

**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

To Patric

Anthony.R.Brown wrote:

It's the same as me Saying N1 = 5 N2 = 4 "Now make N2 = N1" N3 = N1 / N1

Result = N2 = N3 x N1

N1 = 5

N2 = 4

"Now make N2 = N1"

N3 = N1 / N1 "N3 NOW EQUALS 1"

Result = N2 = N3 x N1 " NOW 1 x 5 = 5 " "SO NOW N2 = N1"

Offline

**Dross****Member**- Registered: 2006-08-24
- Posts: 325

Oh, lord - *where do I start!!??*

Firstly - yet * again* you've not responded to my argument at all and to Luca's argument only in an incoherent, vague way. What do you make of them? Where

Secondly - what you have posted above is the worst excuse for a "proof" than I have ever seen in my life. And that includes a lot of sorry excuses for proofs. Now, the first point I'll pick on (the first of many) is this:

Anthony.R.Brown wrote:

A1 + "The 0.1 I put on the side at the beginning "

Some how The original A1 = 1 has become 1.1 and yet at no time was 0.1 ever Add to A1

The two statements here contradict each other - you do the following:

1) Add 0.1 to A1

2) Assert that "at no time was 0.1 ever Add to A1"

I mean, come on! Are we supposed to take you seriously with such blatant inconcistencies as *this*?

*Last edited by Dross (2007-01-31 01:59:42)*

Bad speling makes me [sic]

Offline

**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

A1 + "The 0.1 I put on the side at the beginning "

This is the Original 0.1 not Another 0.1 from somewhere else!

Offline

**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

Everyone must know it's possible to make any Number = 1 as with their examples above!!

N1 = 0.12345612312 N2 = N1/N1 "N2 Now equals 1"

Offline

**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

Two Proof's in One Post! What more could one ask for!!

( 0.9 Infinite "Definition" ) <> 1 ) ( 0.9 Recurring "Definition" ) <> 1 )

Offline

**Dross****Member**- Registered: 2006-08-24
- Posts: 325

Anthony.R.Brown wrote:

A1 + "The 0.1 I put on the side at the beginning "

This is the Original 0.1 not Another 0.1 from somewhere else!

I don't care - you still added it to A1, and then claimed that you never did. This was one of many, many errors in what you posted.

Anthony.R.Brown wrote:

Two Proof's in One Post! What more could one ask for!!

A single sentence that makes sense?

Bad speling makes me [sic]

Offline

**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

A1 + "The 0.1 I put on the side at the beginning "

This is not an additional "Add" this is putting something back! from where it came from!

Offline

**Dross****Member**- Registered: 2006-08-24
- Posts: 325

Anthony.R.Brown wrote:

A1 + "The 0.1 I put on the side at the beginning "

This is not an additional "Add" this is putting something back! from where it came from!

Yes you did put it back where it came from - *by adding it.*

If I take a book off a shelf and say "look, I can put this book back without placing it on the shelf" and then place the book on the shelf, I cannot just say "well, I was just putting it back" - I still had to place it on the shelf now, didn't I?

Anyways, the rest of your so-called-proof made no sense. Please enlighten me as to where exactly (*exactly*, please) mine and Luca's proofs are inadequate.

*Last edited by Dross (2007-01-31 23:09:33)*

Bad speling makes me [sic]

Offline

**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

What no one has done is make! (B1 x C) = (A1 x C) in a Single Calculation!

Because A1 is! and equals 1 and B1 is! and equals 0.9

B1 will always have the 0.1 missing!!

A.R.B

Offline

**Dross****Member**- Registered: 2006-08-24
- Posts: 325

Anthony.R.Brown wrote:

What no one has done is make! (B1 x C) = (A1 x C) in a Single Calculation!

Because A1 is! and equals 1 and B1 is! and equals 0.9

B1 will always have the 0.1 missing!!

A.R.B

Nobody here is trying to show that 0.9 = 1 - we're trying to show that 0.9999... = 1. And we have done so.

And it does not matter what can be done in a single calculation - the proof for, for example, Fermat's last theorem is many pages, but is still perfectly valid as a proof.

**As far as I'm concerned, mine and Luca's last demonstrations that 0.9999... = 1 are valid and true. They conclude this thread as demonstrating that 0.9999... and 1 represent the same number, unless you can find a flaw in them.**

(which you won't... but feel free to try)

Bad speling makes me [sic]

Offline