0.99r = 1

Arnie · 26 Mar 2012 at 11:36

Re the frog:

You're thinking of the centre point of the frog for some reason, just define it as moving 90% of the distance between the end of his front feet and the shore.

Tibbz2 said:
Lol, i've always known it does = 1 This is the way we figured it out:

x = 0.9999999999999etc.
10x= 9.9999999999999etc.

Take them away and you get 9x = 0.9 /9 = 1.

0.999 x 10 = 9.99

9.99 - 0.999 = 8.991

You could argue something similar applies to 0.9r as it's not clear how multiplying an infinite number affects it.

Morbius · 26 Mar 2012 at 11:37

ubersonic said:
Eh?

half of 1 = 0.5
half of .99r = <0.5

Half of 0.9r is 0.49r which is equal to 0.5.

div0 · 26 Mar 2012 at 11:39

Arnie said:
Re the frog:

You're thinking of the centre point of the frog for some reason, just define it as moving 90% of the distance between the end of his front feet and the shore.

True, I could have said that instead. Might have been clearer.

ubersonic · 26 Mar 2012 at 11:40

Morbius said:
Half of 0.9r is 0.49r which is equal to 0.5.

Ok no problem, your right, globally accepted mathematical principles are wrong ^^

Scougar · 26 Mar 2012 at 11:40

Ah... infinity... and beyond!

lukeharvest · 26 Mar 2012 at 11:50

ubersonic said:
If you halve 1 then round it to the nearest whole number its 1, if you halve .99r then round it to the nearest number its 0, ergo they cannot be the same as they don't have the same properties.

0.99... = 1, so they do have the same properties.

dowie · 26 Mar 2012 at 11:52

ubersonic said:
Ok no problem, your right, globally accepted mathematical principles are wrong ^^

erm the previous poster is right and you're being quite silly

Morbius · 26 Mar 2012 at 12:05

ubersonic said:
Ok no problem, your right, globally accepted mathematical principles are wrong ^^

Do you deny that half of 0.9r is 0.49r? Or do you have an issue with 0.49r being equal to 0.5?

You can't say 0.49r isn't equal to 0.5 thus 0.9r isn't equal to 1. That's just using your assumption to prove your assumption.

Gilly · 26 Mar 2012 at 12:07

The video doesn't work for me. Just gets to about a minute and freezes.

daz said:
These threads always go the same way.

People who studied maths up to GCSE = "It's not quite 1, it doesn't matter what maths trickery you use in the 'real world' it's not exactly the same, there'll always be a tiny bit left over"

People who know more maths = "They are the same".

Mathematically the working is sound.

Physically, logically and philosophically they are different.

desires said:
Also i don't like the 'r' notation. 3 dots does the job.

I don't like three dots, I like the triple dot glyph

dowie said:
No its a decimal representation that represents the same Real number 1 (and I did say that earlier.)

Some numbers won't have a unique representation within a given number system.

For example - in say base 4:

0.333r = 1

Is there a number system that will display an infinitesimally small number, such as 0.00r1 (which I understand doesn't exist in our given number system)?

div0 · 26 Mar 2012 at 12:12

Morbius said:
Do you deny that half of 0.9r is 0.49r? Or do you have an issue with 0.49r being equal to 0.5?

You can't say 0.49r isn't equal to 0.5 thus 0.9r isn't equal to 1. That's just using your assumption to prove your assumption.

Although saying that 0.49r=0.5, to prove that 0.9r=1 is also an equally invalid proof.

I think the point he's trying to make (although wrongly), is that 0.999r != 1 because it is less than 1 (in his mind). He then tries to prove this by saying that 0.4999r is less than 0.5 (again wrongly) and so this 'proves' that 0.999r isn't the same as 1.

But again, simply saying that 0.4999r IS equal to 0.5, isn't going to help him understand that 0.99r=1. And it's certainly not a good way to try and prove it either.

Morbius · 26 Mar 2012 at 12:13

Gilly said:
Is there a number system that will display an infinitesimally small number, such as 0.00r1 (which I understand doesn't exist in our given number system)?

There is no such number in any system. If you can put a 1 at the end of an infinite string of zeros, the string of zeros can't be infinitely long.

Morbius · 26 Mar 2012 at 12:16

div0 said:
But again, simply saying that 0.4999r IS equal to 0.5, isn't going to help him understand that 0.99r=1. And it's certainly not a good way to try and prove it either.

I agree, but the intent was to show a circular argument rather than a valid proof. The valid reasons why 0.9r = 1 are already in this thread. There's not much I can really add to them.

Gilly · 26 Mar 2012 at 12:18

Morbius said:
There is no such number in any system. If you can put a 1 at the end of an infinite string of zeros, the string of zeros can't be infinitely long.

I understand that this is the basis of any statement citing no difference between 0.99r and 1. I just wondered if there was a number system that dealt with infinitesimals.

lukeharvest · 26 Mar 2012 at 12:21

ubersonic said:
Ok no problem, your right, globally accepted mathematical principles are wrong ^^

Yes, that's why aircraft don't fly, and we don't send people into space and we can't diagnose/cure many diseases... Also why you're not posting on an internet forum.

lukeharvest · 26 Mar 2012 at 12:23

Gilly said:
I understand that this is the basis of any statement citing no difference between 0.99r and 1. I just wondered if there was a number system that dealt with infinitesimals.

Not really, we have the real numbers, which are uncountable, which is to say, we can't find the term directly after another term, because any term you find there's infinitely many between the two terms.

Morbius · 26 Mar 2012 at 12:30

Gilly said:
I understand that this is the basis of any statement citing no difference between 0.99r and 1. I just wondered if there was a number system that dealt with infinitesimals.

The hyperreal numbers include infinite and infinitesimal numbers, however I don't know a huge amount about them.

div0 · 26 Mar 2012 at 12:34

daz said:
These threads always go the same way.

People who studied maths up to GCSE = "It's not quite 1, it doesn't matter what maths trickery you use in the 'real world' it's not exactly the same, there'll always be a tiny bit left over"

People who know more maths = "They are the same".

Gilly said:
Mathematically the working is sound.

Physically, logically and philosophically they are different.

I would tend to agree with Gilly. I don't think it has anything to do with 'just studying to GCSE level'.

Most people who have a problem with it, just find it hard to accept that adding more and more 9's to the end of the number will eventually 'get to' 1.

And this is a perfectly understandable issue (imo).

Even if you know that 0.999r=1, and even when you know the proof of it, it's still not something that sits naturally with some people. Unfortunately these people just have to learn to accept that it's true, even if they can't quite convince themselves that it's right.

ubersonic · 26 Mar 2012 at 13:19

Morbius said:
You can't say 0.49r isn't equal to 0.5 thus 0.9r isn't equal to 1. That's just using your assumption to prove your assumption.

But it works, see I can prove it, I typed 0.99r into a calculator as much as it would let me and then when I tried to divide it by two it gave an error, because your wrong!

Scougar · 26 Mar 2012 at 13:23

ubersonic said:
But it works, see I can prove it, I typed 0.99r into a calculator as much as it would let me and then when I tried to divide it by two it gave an error, because your wrong!

Well I typed it into a calculator (Windows scientific): 0.999999999999999999999999999999

divided by two

answer it gave: 0.4999999999999999999999999999995

So your's is not conclusive evidence ubersonic. (sorry bud).

div0 · 26 Mar 2012 at 13:24

ubersonic said:
But it works, see I can prove it, I typed 0.99r into a calculator as much as it would let me and then when I tried to divide it by two it gave an error, because your wrong!

I'm not sure if you're trolling now, but you can't type 0.999r into a calculator.

0.999r is not the same as 0.9999999, or even 0.999999999999999999999999999.

0.9999r is just another way of writing 1, if none of the examples shown here convince you of it, just accept it and move on.