1=0.999... infinities and box of chocolates..Phliosophy of Math...

You are confusing the division of integers with the division of reals. I think that the chapter on real numbers comes a little later in the book, have patience, you'll get to it.

 

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You are confusing the equal sign (=) with the greater than sign (>). I think when you get there they will teach you that 1.0 is a whole, while 0.(9) is a fraction of a whole. So your 1.0=0.(9) is false, it is 1.0 is GREATER THAN (>, not =) 0.(9).

 

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lol, read here

 

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Cat got your tongue?

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Originally people were arguing that \(0.\bar{9}\neq1\). As an occasional teacher, I've run into that misconception often.

Then MD argued that \(0.\bar{3}\neq\frac{1}{3}\). I'd never run into that one before, but according to Tach's Wikipedia link, apparently it's a semi-common thing.

Now MD seems to be saying there's no such thing as \(\frac{1}{3}\). I'm at a loss for words.

 

the BIG question though that you need to ask to solve this impasse is :
IF 1 is greater than 0.999.... how much greater is it?

Motor Daddy,
What do you think is the solution to 1 - 0.(9) ?

And if you finally arrive at zero using the conventional mathematics system you will find that 1 = 0.999...

so far we have the conventional and mainstream accepted solution.
1- 0.999... = 0
(this has been proved as calculated as and is generally accepted ~ as terminating at 0)
then we have
1-999... - 1/infinity
this is solution requires mixing mathematical systems and a chocolate out of the box perhaps...

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~ as non-terminating on both sides.

then we have

1-999...= "non-existent"
which is another version of the same thing but with a more material application. IMO ~ as non-terminating on only one side and non-existent on the other

so MD, which would you choose [if any] and why?
What does
1 - 0.999... =
to you?

 

No I think he has misinterpreted, quite accidentally the use of the decimal..
It is amazing and I am just as guilty of it myself how a glaring [to others but not to self] mistake can get stuck in our heads when it comes to understanding something.
1.11 is the same piece of cake as 1.111.... only a marginally bigger version of the same slice. MD considered in one of the posts that they were two different slices.
This sort of misinterpretation of the question can led to significant issues in a persons thinking IMO.

the seemingly simple question:

which one is the larger quantity?
1.11 ml or 1.111... ml

which should read
1.11000.... ml or 1.111... ml

or..

1.11000000000000...
+
0.00111110000000...
=
1.111111100000000...

The "taken for granted" and often not writen, trailing zero's can lead to huge confusion and on the surface it is easy to see how...

 

You mean "mainstream" as opposed to fringe.

Not "conventional", mainstream.

No, "we don't have", only fringers do.

We "don't have" this either, it doesn't exist in mainstream math.

 

Sigh, and no amount of rigorous counterproof will convince them.

 

Chocolate was what I expected but still, nice thing.

 

Do you always repeat what I already wrote or is it just on this occasion?
This is a philosophical thread dealing with the philosophy underpinning mathematics approach to this issue of 0.999...= 1

Perhaps you have a philosophical contribution to share in support of your specialty and demonstrate you actual understanding of what you specialize in.

 

I don't repeat, I point out your errors one by one. The fact that you keep repeating them ad nauseaum triggers the repetition of disproofs.

More like a fringe thread. Wiki characterizes this persistent misconceptions quite well, you should read it.

I did, I proved that \(0.(9)=1\).

 

Just to add,
at age 25 Kurt. F.Godel (1906/78) made incredible philosophical proposition:

re:First incompleteness theorem - wiki: http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

Maybe discussion on this philosophical statement and how it was proved in Mathematics to be founded has some relevance here in this thread.
Especially how it relates to the liars paradox and what that means to science , logic and sound reasoning.

 

You are trying to subtract a non-finite quantity from a finite quantity and expecting to get a finite answer? 1.0 is a whole and .(9) is a percentage of a whole (fraction of a whole).

It's impossible to split an object into 3 equal pieces! At least one of the three pieces has to be different than the other two, they are NOT equal!

 

no you didn't, you only used what others have done and claimed it as your own....
You personally have proved nothing...except that you can use other work by rote.

 

oh, there are many that would agree with you simply on the basis of logic...the use of mathematical limits when working with infinities is due to what reason after all, other than to quantify the unquantifiable, to define the undefinable and to terminate the un-terminatable. IMO [so I do agree with you..essentially]
"to make the infinite finite"
This is why I trend to philosophically believe that

1-0.999... = 1/infinity
As neither side of the equation is terminating and therefore a more natural and intuitive approach to the nature of infinity.
The above is philosophy and not calculation. This is evaluation, using logic that transcends the finite systematization of infinite concepts.

Logically there is no dispute over

1-0.999... = 1/infinity
IMHO

 

...because this is basic math. You should try studying it sometime. Beats trolling this forum with spam.

Envious much?

 

Basic math says that you are wrong, yet you continue to spam the thread. Wonder why?

 

Really? In 8-th grade they teach you how to inscribe an equilateral triangle in a circle. This means that you either haven't taken that class yet or that you flunked it.

 

So if the triangle has an area of 100 sq. in. and you divide the triangle into pieces of 33.(3) sq. in., how many pieces do you have?