Post me your hardest maths question you know

x = 0.9r

10x = 9.9r

9x = 9.9r - 0.9r

9x = 9

x = 9/9

x = 1

I had a think about this earlier today, and my thinkings on it are as follows.

When you have any decimal (and in your case 0.9 reoccurring)

and it is then multiplied by 10, lets use 0.02 for example

all the numbers shift to the left

so 0.2. Fine I think we all know this.

However in your question.

think of it like this 0.999999999999999999999999 goes on to infinite amounts of decimal places.

so imagine 0.9999 ............. 999{9}(9) [9]

[9] = the infinite decimal number
(9) = the (infinity - 1) decimal number
{9} = the (infinity - 2) decimal number
And so when you multiply by 10
you get:

0.9999 ............ 999{9}(9)[0]

And when you take that from 9.999 reoccurring

you are not left with 9

you are left with:

9.0000 ............... 00{0}(0)[9]
and then when you divide by 9 you are also left with
1.0000 ............... 000{0}(0)[1]

and not 1.

thoughts please?


I understand that if it is reoccurring then it never reaches the end,

and because of this I believe infinity to be a constantly changing number, however this doesn't disprove my point.

If somehow you were to freeze a reoccurring number in an instant of time then you would find the infinite decimal place.
 
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Tell me, what is 1 - 0.9r?

An inexpressible number. That doesn't prove your point. 1/3 is simplified to 0.3r in decimals but that is just that, an approximation. The idea of recurring is to express the fact that we cannot represent the number accurately.

Think of it this way. If 0.9r = 1 then at what point does it equal 1. Recurring relates to the infinite nature of the value recurring, so how can something that by its very nature has no set value equal something that does have a set value.

The only way that 0.9r = 1 is in theoretical maths.
 
An inexpressible number. That doesn't prove your point. 1/3 is simplified to 0.3r in decimals but that is just that, an approximation. The idea of recurring is to express the fact that we cannot represent the number accurately.

Think of it this way. If 0.9r = 1 then at what point does it equal 1. Recurring relates to the infinite nature of the value recurring, so how can something that by its very nature has no set value equal something that does have a set value.

inexpressible? I think not. It is

Limit as n tends to infinity of: 1/(10^n)

also known as 0
 
I think this is where you run into trouble. ;)

Why?

infinity - infinity is 0.

Infinity - infinity + 1 is 1.

I don't see why that's wrong, if you read the rest infinity is never ending and so when I say infinity it is at the end, regardless, and the -1 just means the decimal place before it.
 
An inexpressible number. That doesn't prove your point. 1/3 is simplified to 0.3r in decimals but that is just that, an approximation. The idea of recurring is to express the fact that we cannot represent the number accurately.

Think of it this way. If 0.9r = 1 then at what point does it equal 1. Recurring relates to the infinite nature of the value recurring, so how can something that by its very nature has no set value equal something that does have a set value.

The only way that 0.9r = 1 is in theoretical maths.

We can represent it accurately: we invented the 'recurring' notation to represent it. 1/3 === 0.3r. It's by definition of what the 'r' means.

You need to understand that there's many different ways of writing down an expression that equals the same numerical concept. You could choose to rewrite '1' as 'e^(i*pi) + 2', or '2*integral[0->1](x dx)' or '3*1/3' or '0.9r'. They're all equivalent representations of the concept we commonly refer to as '1'. They're not approximations, they're definitively equal.

Seriously, smarter people than us all disagree with you.
 
The only way that 0.9r = 1 is in theoretical maths.

Right, and since this whole discussion doesn't make sense outside the context of "theoretical maths" (which is actually just maths), we can conclude that indeed 0.9r = 1. You can't just say "let's ignore maths" when talking about mathematical problem.

Anyone who disagrees with this is categorically wrong and simply doesn't understand the question. You can disagree with mathematical truths all you want, but that just makes you wrong.

It's essentially the same as arguing that 1.0r does not equal 1 because they're written differently.
 
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Infinity doesn't work like that.

How does it work?

it is a theory anyway.

And if infinity is the end, then there has to be a number before it,

it can't just count like:

1, 2, 3, 5 billion.

there has to be a number before it Always, just like there is always a number before any number. (except negative infinity)
 
How does it work?

it is a theory anyway.

And if infinity is the end, then there has to be a number before it,

it can't just count like:

1, 2, 3, 5 billion.

there has to be a number before it Always, just like there is always a number before any number. (except negative infinity)

Infinity isn't a number. The concept of a 'number before infinity' makes as much sense as the concept of 'Wednesday tasting of bacon'.
 
All this talk makes me wish I chose to do Degree level maths,

Doing my A-Levels atm but chose to do Computer Science at university, I love both computing + maths but which to choose was tough.

I guess it was just because I had done maths all my life.
 
All the time! 0.9r only has one value.

Thats a little pedantic. Of course 0.9r is the value 0.9r. But you would never hit the value 1 with 0.9r. You cannot express a number between 0.9r and 1 but I can't see how that is relevant.

That is a little akin to saying "using whole numbers, give me a number between 5 and 6. It can't be done.

The nature of infinity means that it will never hit the next number in the sequence. 0.9r will never be 1 until you get bored and round.
 
Thats a little pedantic. Of course 0.9r is the value 0.9r. But you would never hit the value 1 with 0.9r. You cannot express a number between 0.9r and 1 but I can't see how that is relevant.

That is a little akin to saying "using whole numbers, give me a number between 5 and 6. It can't be done.

The nature of infinity means that it will never hit the next number in the sequence. 0.9r will never be 1 until you get bored and round.

THEY ARE DEFINITIVELY THE SAME THING. THAT'S WHAT 'RECURRING' MEANS.

ARGLEGELUHALHGLAH

P.S. the inability to find a real number between two numbers is the definition of those two numbers being the same.
 
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