0.9999....(recurring) = 1?

George,Y · 2007-01-26 23:07:40

What I mean is that what we focus should be on the truth, not the beauty. Because aethetic feelings are untransendable-you can have yours, and I can have mine, while maths concept, so far, are uniform around the world.

That is definately due to its power to again and again successfully apply to the real world, its correctness, its right reflection of the reality (the facts).

So I scincerely call on you not to talk about beauty, the additional and unnecessary charactor of maths. 200! may be too long and thus ugly, but we cannot deny that is correct and in fact so that we must accept it.

MathsIsFun · 2007-01-26 23:11:11

OK, but there is the saying "beauty is in the eye of the beholder", which roughly means that each person has their own idea of beauty and so it is hard to debate, I suppose.

So, let truth reign! And let each person see beauty where they can.

George,Y · 2007-01-26 23:14:20

MathsIsFun wrote:

Oh, well I was commenting on how nice the concept of repeating decimals was ... how it all "hangs together".
I think the important thing is to know that decimal numbers are just a common way of representing numbers.
For example, instead of saying 1=1.000... we could use an infinite series:
And likewise, instead of saying 1=0.999... we can write:

You discussed mainly about the advantage of and your preference on the concept of infinity.

While if one thing has its advantage, it may bear a disadvantage as well. Moreover, its counterpart may have another advantage. I have illustrated both its disadvantage(its dilema, contraversary) and the alternative theory (small error theory, in many cases, fact) in the previous posts. So perhaps one can choose which to use.

The second, preference, its upon individual's free choice, too.

Anthony.R.Brown · 2007-01-27 01:54:35

To kylekatarn

QUOTE:

" 1 = 1.0 = 1.00 = 1.000 = ... = 1.(0) "

...and it's beautiful, isn't it? ^^"

ARB

I dont know about beautiful! It might have been Good! if only it was a Counter Proof to the Fact! that I can Take away the Decimal Point Concerning 1.0 and it will still = 1
But if I do the same with 0.333... or 0.999.. then they both end up Completely Different Numbers!!

MathsIsFun · 2007-01-27 10:52:13

George,Y wrote:

... I have illustrated both its disadvantage(its dilema, contraversary) and the alternative theory (small error theory, in many cases, fact) in the previous posts. So perhaps one can choose which to use.

Yes. In fact I had a calculus professor who loved teaching in terms of infinitesimals (which are not zero, but less than any real number) just like Newton's original work. And I was also taught limits (considered more rigorous).

And I believe there are modification to infinitesimal calculus that do make it rigorous (hyperreal numbers), so an old theory lives again!

And that is a good thing about mathematics: we can entertain different theories and see their benefits and disadvantages.

Ricky · 2007-01-27 11:39:26

That is definately due to its power to again and again successfully apply to the real world, its correctness, its right reflection of the reality (the facts).

I have asked many times, George, and as long as you make the above statement, I will continue to ask it. Where does infinity exist in reality? If it doesn't, then you are of the opinion that infinity should not be included in math. Is this correct?

George,Y · 2007-01-27 23:44:10

Astrology also have marvellous assumptions and bewildering deductions. What do you think that makes maths more convincing than astrology, Ricky?

Patrick · 2007-01-27 23:57:39

George, Y - As I told you in the other 0.(9)=1 thread, mathematics is nothing but a system logically derived from some axioms. Therefore, if something is true according to the axioms, it's true in mathematics. You could of course change some axioms, but that would change mathematics totally, and you'd be left with a whole new system. You're totally welcome to create your own system, based on the real world, but then you'd need to discuss it somewhere else than this forum - or atleast make it clear what you were talking about. The bottomline is - math does not depend on the 'real world', nomatter how neatly you can use math to solve problems in it.

George,Y · 2007-01-28 00:28:06

Well I may reply to your bottomline on the other thread.

Ricky · 2007-01-28 07:14:27

Astrology also have marvellous assumptions and bewildering deductions. What do you think that makes maths more convincing than astrology, Ricky?

The entire embodiment of astrology does not have a single deduction, George. Astrology is filled with non sequiturs, and anyone who thinks otherwise will probably not be an accepted member of any math or scientific community.

Anthony.R.Brown · 2007-01-29 00:58:48

So there we have it! Looks like The Cambridge Advanced Dictionary/Thesaurus has Defeated everyone on this Post!

The Equation below sums up everything in a Nice way!!

( 0.9r "Definition" ) <> 1 )

A.R.B

Patrick · 2007-01-29 01:23:53

Anthony.R.Brown wrote:

So there we have it! Looks like The Cambridge Advanced Dictionary/Thesaurus has Defeated everyone on this Post!
The Equation below sums up everything in a Nice way!!
( 0.9r "Definition" ) <> 1 )
A.R.B

Why don't you try to submit some of your great ideas to a journal and have it peer reviewed?

Anthony.R.Brown · 2007-01-30 02:12:09

To Patrick

Quote:"Why don't you try to submit some of your great ideas to a journal and have it peer reviewed?"

A.R.B

Dont worry they will come knocking soon!!

Patrick · 2007-01-30 03:56:47

Please notify me. When I come to think about it, weren't you the one with the "all problem"-solving algoritm?

luca-deltodesco · 2007-01-30 04:10:20

yes he was i believe that was also rather funny

Dross · 2007-01-30 04:13:47

What was the "all-problem solving algorithm" you speak of?

luca-deltodesco · 2007-01-30 04:15:12

he believed hed found some magical algorithm, that could solve ANYTHING accross ANY field of mathematics NO MATTER WHAT, and that he'd used it to proove all the millenium math problems

Dross · 2007-01-30 04:24:27

And of course, he wouldn't tell us this algorithm as we'd just use it for our own financial gain?

luca-deltodesco · 2007-01-30 04:27:42

yeh thats the one

Patrick · 2007-01-30 04:28:33

Correct I wonder if he's still working on that

Zhylliolom · 2007-01-30 08:01:21

The member who posted about the "all problem solving algorithm" was se7en. This is the guy you're talking about, correct?

http://www.mathsisfun.com/forum/viewtopic.php?id=4028

He deleted most of what he said, but you'll probably remember the thread if we are thinking of the same guy.

luca-deltodesco · 2007-01-30 08:57:05

ah well, it was a similar kind of scenario though

Patrick · 2007-01-30 08:58:53

ah darn

Anthony.R.Brown · 2007-01-30 23:34:48

( 0.9r "Definition" ) <> 1 ) "Now that,s Beautiful!"

A.R.B

Dross · 2007-01-31 02:01:41

Anthony.R.Brown wrote:

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!

Erm... yes, Anthony... whatever you say...

Math Is Fun Forum

#301 2007-01-26 23:07:40

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#302 2007-01-26 23:11:11

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#303 2007-01-26 23:14:20

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#304 2007-01-27 01:54:35

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#305 2007-01-27 10:52:13

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#306 2007-01-27 11:39:26

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#307 2007-01-27 23:44:10

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#308 2007-01-27 23:57:39

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#309 2007-01-28 00:28:06

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#310 2007-01-28 07:14:27

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#311 2007-01-29 00:58:48

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#312 2007-01-29 01:23:53

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#325 2007-01-31 02:01:41

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