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 Scarfacé
they seem to create all these lame theorys that currently defeat simple laws of logic. Currently infinity only exists within numbers, right?
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Yeah, they just sit around creating ideas to confuse people. In my lectures they don't teach maths, they just give us a lot of funny looking symbols to use to confuse other people. Its all a big scam :p
 
rach676-threads.jpg


As posted in previous thread.

:p
 
Originally posted by <Ry@n>
Surely as the "r" means never ending 9's, and just cos u dont ever get to see the end of the 9's, doesnt mean they dont exist. So it cant = 1.
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As has been said before:

0.9
0.99
0.999

The space between those values and 1 is:

0.1
0.01
0.001

respectively

But in:

0.9r

There is no space left over because the 9s never end.

All of the 9s take up all of the space between 0 and 1, thus making it the same as 1.

Really the most obvious way of demonstrating that 0.9r = 1 is:

1/3 = 0.3333r

0.3333r *3 = 0.9999r

1/3 * 3 = 1

This shows that 3/3 is at the same time both 0.9r and 1.

edit: corrected a mistake
 
Last edited:
Originally posted by growse
You mean it defies logic because you don't understand it?

Can the people who say 0.9r doesn't equal 1 explain to me how 4+5 doesn't equal 9?
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Probably I don't understand this Mathmatical invented theory, no.


0.9r is 0.*everlasting line of 9's*

Yes, if so.. it's never quite 1, yes?


How does maths prove otherwise?
 
Why are people still arguing that 0.9r does not =1 when people like alpha have provided numerous proofs that in fact it does.
If anyone disagrees with the proofs please post your own proof which shows it doesn’t, all I have seen is people who cant understand the answer, so say no it doesn’t it cant be, well that’s a great argument and I am surprised people like alpha have managed to keep his cool.
:)
 
Originally posted by Shadez
Equal = Having the same quantity, measure, or value as another.

Equivalent = Being essentially equal, all things considered:
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So what's missing in the equivalent definition that's not "essential"?

8 essentially equals 9 therefore. To the nearest 9?
 
Originally posted by Pious
As has been said before:

0.9
0.99
0.999

The space between those values and 1 is:

0.1
0.01
0.001

respectively

But in:

0.9r

There is no space left over because the 9s never end.

All of the 9s take up all of the space between 0 and 1, thus making it the same as 1.

Really the most obvious way of demonstrating that 0.9r = 1 is:

1/3 = 0.3333r

0.3333r * 0.3333r = 0.9999r

= 1/3 * 1/3 = 3/3 = 1/1 = 1

This shows that 3/3 is at the same time both 0.9r and 1.
Click to expand...

Sums it up nicely (No pun intended)









:rolleyes:
 
Originally posted by cymatty

If anyone disagrees with the proofs please post your own proof which shows it doesn’t
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See, this is the cool thing about maths. If you can find just one counter example, then the whole idea of 0.9r=1 is thrown off. Likewise, our concepts of "stupidly small to any normal person" are thrown off. So please, somebody construct a mathematical counterproof.
 
Originally posted by growse
So what's missing in the equivalent definition that's not "essential"?

8 essentially equals 9 therefore. To the nearest 9?
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I strongly suspect he's insinuating rounding up.

Again, math in its purest form (such as this) does not translate well to the real world! Mathematically, 0.9r=1, full stop.
 
Cheers Growse/Alpha, at least I know that i've got a very basic idea of this incompletness stuff :)

To sum up, the axioms are accepted to be true, but might lead to inconsistancy somewhere down the line. However, in the simple proof

x = 0.9r
10*x=9.9r
10*x - x=9.9r - 0.9r
9x = 9
x=1

Its either impossible for these contradictions to pop up, or very very unlikely.

Is that about the size of it?


Got a book on order on the subject actually, allegedly it explains it well in laymans terms, will be very interested to see what it says. As with most things that I pick up in passing, generally when I read a proper book dedicated to the subject, I end up realising that I've been talking rubbish!

Anyway, another question :

Given that 0.9r=1 ( which I believe it does ), and 1=1, and also that 1.0r=1, how many ways are there ( in a strictly mathematical sense ) of defining unity, or any given number?
 
Originally posted by Scarfacé

0.9r is 0.*everlasting line of 9's*

Yes, if so.. it's never quite 1, yes?
Click to expand...

Stop trying to imagine a long list of 9s. No matter how big the list is in your head it isnt even close to 0.9r. This is where all your thinking is wrong. Just accept that the 9's go on infinately, it is for this reason that it precisely equals 1.

To repost a proof


x = 0.9r
***10x = 9.9r***
10x - 1x = 9.9r - 0.9r
9x = 9
x = 1


For me the ***ed part is the important part of the proof. When you multiply 0.9r by ten you move the decimal point 1 place left, with a normal decimal multiplication there would therefore be 1 less digit after the decimal point. Since the 9s go on to infinity even when you move the decimal point left there are STILL an infinate number of 9s after the decimal point.

Get me?
 
Originally posted by GTA
Given that 0.9r=1 ( which I believe it does ), and 1=1, and also that 1.0r=1, how many ways are there ( in a strictly mathematical sense ) of defining unity, or any given number?
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You can define numbers by equations (ie their behaviour in systems), so I imagine there are an infinite number of ways of defining any number.
Originally posted by GTA
To sum up, the axioms are accepted to be true, but might lead to inconsistancy somewhere down the line
Click to expand...
Yes, and if they do, they are altered till no inconcistencies arise. So far, we've managed 400 years of "analysis" without anyone finding a problem :)
 
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