Poll: Does 0.99 Recurring = 1

Does 0.99 Recurring = 1

  • Yes

    Votes: 225 42.5%

  • No

    Votes: 304 57.5%
  • Total voters
    529
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Originally posted by TwoWheelTerror
damn.. I've had inspiration and need to change my vote


pi is an irrational number.. with the most rational number for pi being 22/7

the most rational number for .99r is 1
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you can find more a closer rational approximation to pi then 22/7, so it isnt the most rational number for pi

and you have missed the point, 0.9r=1, it is not "the most rational number for 0.9r" it is exactly one
 
Originally posted by AlphaNumeric
You need an infinite amount of points to form any smooth curve :)
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i understand this and the what the definition of a circle and also a smooth curve

your missing my point, i saw the point raised that 0.0000r1 plus 0.9r is equal to one and not 0.9r so i was saying do these people also believe that there is no such thing as a circle just a lot of points and also for the people saying infinite number of anything doesnt exist
 
Originally posted by AlphaNumeric
You can find as many as you like, each one better than the last ;)
3, 31/10, 314/100, 31415/1000, 314159/100000 etc etc :)
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going off topic i never said you couldnt, or there was one which was "the most" rational approximation for pi
 
Originally posted by Kyle Reece
[B
0.9r is equal to 1 only in a mathematical context.In the same way that the true number for pie is only useful in a pure mathematic environment. The rest of us are quite happy with pie being 3.14.

In practical terms, real world terms, logical thought terms, and sheer common sense terms, 0.9r is equal to 0.9r and nothing else.

[/B]
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Actually in the practical real world (as you so call it) i doubt people use the term 0.9recurring. Maybe 0.99 pounds but not 0.99r. 0.99r is something that would only be needed in that other world, the world of science (which apparantly is different to the real world).

Just because something doesnt follow your common sense doesnt mean its wrong or cant happen. Its this kind of thinking that has really held humanity back over its existance.

If you think 0.9r=1 is peculiar you should stay a way from quantum physics, where things really defy common sense. I won't go into a specific example but i suppose an equivilant poll could be does the data=0 or 1 or both 0 and 1 at the same time? Here nothing is certain only probably. You could try to write quantum physics off as something obscure, that could never effect the world we see around us. But even this very strange bizzare effects are being put to use in a completly new generation of computers, which may in a couple of decades, end up being used to by people to log onto a computer forum and argue about whether or not 1=1! But hopefully we'll have a bit more common sense by then.
 
Originally posted by AlphaNumeric
Any recurring decimal is infact rational. I can prove it if you want?
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Could you please, not entirely relevant to the thread but i've seen it done before and cant quite remember the steps...

It's quite similar to the x=0.9r , 10x = 9.9r , etc etc etc proof IIRC



Pete
 
If you have a scientific calculator.

Put in 1/3 and multiply it by 3... It equals 1.

Put in 1/3 again, then press the A b/c button (which converts it to fraction). So you have 0.3333333333. Multiply that number by 3 and you get 1. So 0.3333333 recurring x 3 is Exactly equal to 1.

Type in 0.333333333333 x 3 (which isn't recurring) and you get 0.999999999999999.

If you accept 0.3333333 recurring x 3 = 1

Then 0.9999999999999 recurring = 1 (as 0.333333 recurring x 3 = 0.999999 recurring).
 
Originally posted by yak.h'cir
You could try to write quantum physics off as something obscure, that could never effect the world we see around us.
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Its the most accurate (ie squares up with experimental results) model of the universe we've (humans) have ever made. Predictions for the behaviour of systems of particles are in agreement with experiments down to 10 decimal places. Newton's Gravity screws up at about the 4th decimal place.

Its got little to do with common sense too. Even some of the "basic" ideas aren't what most people would think of as correct. In Quantum Mechanics ab != ba. Its non-commutative algebra.
With "usual" numbers you get things like 3x5 = 5x3. No problem. Once you meet matrices you realise that not everything is so nice. Quantum Mechanics is based on such "non-nice" things.
Originally posted by Grrrrr
Could you please, not entirely relevant to the thread but i've seen it done before and cant quite remember the steps...

It's quite similar to the x=0.9r , 10x = 9.9r , etc etc etc proof IIRC
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Suppose a number is K = 0.ABC.....XYZABC.....XYZABC.....XYZ...... etc

Where A,B,C, X, Y, Z are single digits, ie 1/7 = 0.142857142857.... so A = 1, B = 4 etc

There are "n" digits before repetition begins.

K = 0.ABC.....XYZABC.....XYZABC.....XYZ......
K * 10^n = ABC......XYZ.ABC......XYZABC.......
(K * 10^n) - K = ABC......XYZ (a whole number)
K (10^n - 1) = ABC......XYZ
K = (ABC......XYZ)/(10^n - 1)

Since K is a repeated decimal, n is not infinite, therefore 10^n - 1 is not infinite either, thus ABC.....XYZ/(10^n - 1) is a finite integer over another finite integer, otherwise known as a rational number :)

I apologise if is appears crud, as I've said before, forum text is crap for maths symbols and explainations :(
 
Originally posted by yak.h'cir
0.99r is something that would only be needed in that other world, the world of science
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I honestly can't see a scientific application for it. Even a mathematical use for it, apart from telling people that it equals one ;).

If you think 0.9r=1 is peculiar you should stay a way from quantum physics, where things really defy common sense.
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I used the term "common sense" subjectively to how I'd define my common sense. Physics tells you that you can walk through solid objects, my common sense tells me I can't.

pull philosophy into a discussion about mathematics
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I must have missed the qualifier in the question that the discussion was only about maths ;)
 
Originally posted by Kyle Reece
Even a mathematical use for it, apart from telling people that it equals one ;).
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Obviously don't do enough maths then. I regularly do problems which require the use of infinite sums, resulting in integers, exponentials and trignometic functions.
 
Originally posted by Kyle Reece
And in those cases you have to use 0.9r or 1?
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An infinite sum results in suming 0.9, 0.09, 0.009 etc etc, which I replace with 1 for convenience. I could quite happily keep the infinite sum sign, it behaves exactly like 1 does, being 1 and all, but I'm a lazy kinda guy and I find writting "1" easier on the arm than "Sigma i=1, infinity [0.9^i]" all the time :p
Originally posted by Obl][vion
Alpha, you should come out with me and get battered at the weekend, you must be tired of hitting that reply key ;) :D
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I'm 21 on Thursday, I'll be getting sufficently battered then ;)
 
Originally posted by Kyle Reece
So you don't actually use the equation discussed? You use the assumption based off it.

OK, thanks for clearing that up and proving me right ;)
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So I prove within a mathematical context that 0.9r = 1, then use that proof in a mathematical context. Where did I prove you right there?

After all, I do all my work in a mathematical context, being a maths student and all.
 
I'll make it clear :D Most Humans round up by 1, so 99p is £1 to most, only a few will make it point, Superman 3 "I think, Richard Pryor" was point of show, only a few will notice it, most prob wont...... if such and such earns 5.99 an hour, he wont miss a 0.01 add them all up over a mss and its mega...... well I am thick person, but makes sense to me..... :D flames await
 
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