Post me your hardest maths question you know

I understand the mathematical proof that 0.9r = 1 but I will never be convinced that the two are the same. We simplify 1/3 of 1 to 0.3r as it is impossible to represent it accurately.

Little point in continuing the discussion as I feel we are operating from different standpoints.

To summarise

Technically, 0.9r is not 1. Only 1 is one. The decimal representation of 1 is 1.0r.

1/Infinity represents an infinitesimal quantity, to use the term from earlier in the thread. It is approximately 0, but not equal to zero.

You can't say it equals zero because of the numerator; there is a 1 there, which denotes a quantity.

Don't get me wrong, I understand the reason that it is accepted that 0.9r equals 1, but in purely technical terms and precise math, it isn't truly equal.
 
fez said:
If you are working under the assumption that 0.3r = 1/3 of 1 then yes, 0.3r = 1/3 of 1.

I was under the impression that recurring represented the fact that there are an infinite number of the recurring value.

So 0.3r was the same as 0.33333.... with an infinite number of 3s. If that is the case then 0.3r * 3 will never exactly equal 1.
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I think you're confused, 'infinite number' doesn't mean there's a countable number of 3s, it just means that the amount of 3s has no end.

However if you're that worried about getting an exact, countable decimal answer for this problem, you can always use base-3.

decimal operation: 10/3 = 3.3r
in base-3: 101/10 = 10.1
 
fez said:
I understand the mathematical proof that 0.9r = 1 but I will never be convinced that the two are the same. We simplify 1/3 of 1 to 0.3r as it is impossible to represent it accurately.

Little point in continuing the discussion as I feel we are operating from different standpoints.

To summarise

Technically, 0.9r is not 1. Only 1 is one. The decimal representation of 1 is 1.0r.

1/Infinity represents an infinitesimal quantity, to use the term from earlier in the thread. It is approximately 0, but not equal to zero.

You can't say it equals zero because of the numerator; there is a 1 there, which denotes a quantity.

Don't get me wrong, I understand the reason that it is accepted that 0.9r equals 1, but in purely technical terms and precise math, it isn't truly equal.
Click to expand...

It's not 'accepted', it's 'proven'. There's a bit of a difference

If only '1' is one, what's -e^(i*pi)?
 
Lightnix said:
I think you're confused, 'infinite number' doesn't mean there's a countable number of 3s, it just means that the amount of 3s has no end.

However if you're that worried about getting an exact, countable decimal answer for this problem, you can always use base-3.

decimal operation: 10/3 = 3.3r
in base-3: 101/10 = 10.1
Click to expand...

I understand the idea of infinite but while you have an infinite number of 3's in your 0.3r, they will never make any difference to the fact that you will never truly make 3 * 0.3r hit 1.0.

How can a number 0.9r equal 1.0r. As above, 1 divided by infinity is not 0 which is what you are essentially arguing.
 
fez said:
I understand the idea of infinite but while you have an infinite number of 3's in your 0.3r, they will never make any difference to the fact that you will never truly make 3 * 0.3r hit 1.0.

How can a number 0.9r equal 1.0r. As above, 1 divided by infinity is not 0 which is what you are essentially arguing.
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You quite clearly don't understand the concept of 'infinity'.

How can "110 base 2" equal "6 base 10"? They look different, so they must be different, right?
 
Milkybk said:
Has the OP actually answered any questions yet? He seems to be simply posting his own and then debating mathematical topics. Does Google not know all the answers like you were hoping for?
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Regardless, it's sparked interesting debate on a topic I love so I don't care.
 
fez said:
I understand the idea of infinite but while you have an infinite number of 3's in your 0.3r, they will never make any difference to the fact that you will never truly make 3 * 0.3r hit 1.0.

How can a number 0.9r equal 1.0r. As above, 1 divided by infinity is not 0 which is what you are essentially arguing.
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fez, you're wrong.

I think the root of your misunderstanding is that you're thinking in terms of processes and time. You interpret 0.9r as being built by iteratively adding a 9 to the end of "0." infinitely many times. You say that you'll "never hit 1" by doing this, and you're right, since "never" implies a finite number of steps. However since there are infinitely many 9s, we have by construction already "hit 1". If you like, the concept of infinity overcomes the "never" that you talk about.

This process of "building" 0.9r by adding digits successively is simply a rather crude interpretation of what 0.9r actually means.

What you should understand is that 0.9r is, by construction, equal to 1. That it has two different representations is just an artefact of the decimal notation we use.
 
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growse said:
You quite clearly don't understand the concept of 'infinity'.

How can "110 base 2" equal "6 base 10"? They look different, so they must be different, right?
Click to expand...

Oooh, I think I understand now but 4 + 2 will never be the same as 3 + 3.

Or sorry, I thought we were just being stupid.
 
fez said:
So infinity doesn't refer to something that has no end? Something that is not quantifiable?
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fez said:
I understand the idea of infinite but while you have an infinite number of 3's in your 0.3r, they will never make any difference to the fact that you will never truly make 3 * 0.3r hit 1.0.
Click to expand...

If you understood what infinity was, you'd understand why the phrase 'trying to make 3*0.3r hit 1' is utterly misguided and meaningless.

You don't 'hit' infinity.


fez said:
Oooh, I think I understand now but 4 + 2 will never be the same as 3 + 3.

Or sorry, I thought we were just being stupid.
Click to expand...

Pretty much exactly what you're asserting with your 0.9r!=1 nonsense.
 
One final question to see if we are even on the same page.

What is 1 divided by infinity?
 
fez said:
One final question to see if we are even on the same page.

What is 1 divided by infinity?
Click to expand...

You can't divide by infinity. It's not a number

let's divide 1 by cow.

However you can do f(x) = 1/x

and as x -> infinity, f(x) -> 0
 
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