0.99r = 1

GhostlyPea said:
Makes more sense ta. Somebody else posted 1/3 = 0.33r which we accept but ofc 0.333r x 3 = 0.99r which leaves us in the same situation as people accept 3 x 1/3 to equal 1 but not when written as 0.33r x 3. Am I right in thinking we can't display the "missing" bit as a fraction as it can't be quantified?

I just wish I understood Maths better - I only have a GCSE as I wasn't able to do it at A-Level. I want to attend evening classes but time restraints and all that...

- GP
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There is no "missing bit". The two numbers are equivalent, interchangeable, identical.

Two numbers are defined as being different if it's possible to identify a number that exists between them on the number line. If you can't do that, then the two numbers are the same.
 
For those struggling to understand, remember that 0.9r is purely a mathematical term, it can never exist in the real world. Everything in the real world is finite.
 
growse said:
There is no "missing bit". The two numbers are equivalent, interchangeable, identical.

Two numbers are defined as being different if it's possible to identify a number that exists between them on the number line. If you can't do that, then the two numbers are the same.
Click to expand...

I understand there's no missing bit, I was just using the "" to identify what I was talking about, but yes your second sentence solidifies what I was referring too.

Next question -

Does this hold true with recurring numbers where the recursion(?) is trailing another digit after the decimal point (assuming I have notated below correctly)

i.e. Does 0.199r = 0.2

This seems to follow the same rules if I'm right?

- GP
 
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div0 said:
So if a frog is in the middle of a lake and with every hop he jumps 90% of the remaining distance to the edge of the lake. Does he ever reach the other side?

Apparently yes, if he lives to be infinitely old.
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No, because in this case the lake (our number system) is infinite length, he just jumps forever whilst never getting to the other side (which represents 1).

My brain hurts now. :p
 
I understand people not understanding it, but after it has been explained (and proved) by myself and other mathematicians on the forum, people still disagreeing must either by trolling, or are just seriously stupid. If you don't believe it to be true, clearly you don't know much about mathematics, which makes me wonder why you're even arguing the point anyway.
 
SlyReaper said:
It's incredibly simple; subtract 0.99r from 1, and you get 0.00r, which is equal to 0.
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Nice.

For anyone who doesn't understand why 0.99r = 1 then consider what could possibly remain from 1 - 0.99r?

lukeharvest said:
I understand people not understanding it, but after it has been explained (and proved) by myself and other mathematicians on the forum, people still disagreeing must either by trolling, or are just seriously stupid. If you don't believe it to be true, clearly you don't know much about mathematics, which makes me wonder why you're even arguing the point anyway.
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It is quite ridiculous. Mathematicians who understand what's going on know that 0.99r = 1 so why people without the appropriate skills feel the need to argue the point is beyond me.
 
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GhostlyPea said:
I understand there's no missing bit, I was just using the "" to identify what I was talking about, but yes your second sentence solidifies what I was referring too.

Next question -

Does this hold true with recurring numbers where the recursion(?) is trailing another digit after the decimal point (assuming I have notated below correctly)

i.e. Does 0.199r = 0.2

This seems to follow the same rules if I'm right?

- GP
Click to expand...

Yep.

0.199... = 0 + 1/10 + 9(1/10)^2 + 9(1/10)^3 + ...

= 0 + 1/10 + 0.9(1/10) + 0.9(1/10)^2 + ...

= 1/10 + 0.9*(1/10)/(1-1/10)

= 1/10 + (9/100)/(9/10)

= 1/10 + 1/10

= 0.2
 
Glaucus said:
For those struggling to understand, remember that 0.9r is purely a mathematical term, it can never exist in the real world. Everything in the real world is finite.
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I think the problem some people have, including some who claim to know the right answer, is that the answer doesn't always make sense in the real world.

Hence the reason I made my previous post, even just as a bit of a joke.

If the frog was 1m from the edge of the pond and with every jump he covers 90% of the remaining distance, then the distance he jumps can be shown to be:

0.9m
0.99m
0.999m
.
.
.
0.999.....m

Obviously the fact that the frog isn't infinitely small (as someone rightly pointed out), would mean that eventually his size is greater than the remaining distance. But if we could somehow conceive an infinitely small frog, in the above example, the frog should still never reach the other side. He'll keep getting closer, but never quite get there.

This is a 'real world' example, where the concept of infinity leads to a mathematical result (0.9999r=1) that doesn't sit well with the observable 'real world' pattern (0.99999.....never quite gets to 1).

And I think that's the crucial point that some people find hard to accept.
 
Its not a real world example as you've made the frog infinitely small. You also have minimum movement due to size limitations of atoms and everything else.
It's a pure mathematical term that arrives as we can just think up any number. It doesn't actually exist in the real world. Which is why thinking about it in terms of real world is what creates the confusion, it needs to be thought off in pure maths terms, the only place you will ever find it.
 
Suppose we have two different real numbers, a and b. Then a-b=c, where c is a non-zero real number.

1-0.9r = 0, so by the contrapositive 1 and 0.9r are the same.
 
sniffy, the answer to you question about 1 - 0.99r... the answer would really be 0.00r, because we cannot give an end point for 0.99r neither can we give an end point for the remainder.

As I discussed a few posts above, I perceive it to be a problem with representation of numbers and NOT maths itself.

If 0.99r is the result of a calculation it would probably be better to accept it as 1. If it's 0.99r by itself, then that's not the same as one, but once again probably better to accept it as 1.

If you can think of a way to represent recurring numbers in decimal you will solve this issue ;-) (other than 'rounding up and down').
 
Glaucus said:
Its not a real world example as you've made the frog infinitely small. You also have minimum movement due to size limitations of atoms and everything else.
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No, I totally agree. Making the frog infinitely small maybe confused the point I was making. But I was trying to show that you need to separate the mathematical concept from the observable pattern.

When you think of the observable pattern:

0.9
0.99
0.999
.
.
.
0.99999......

It is easy to follow that pattern and say that it doesn't matter how many 9's you add to the end, you will never get to 1. And this is true.

But 0.999r is purely a mathematical concept. There is no way to 'get to' 0.9999r, just by 'adding 9's'. The whole concept of infinity means that you will never 'get there'.


Glaucus said:
It's a pure mathematical term that arrives as we can just think up any number. It doesn't actually exist in the real world. Which is why thinking about it in terms of real world is what creates the confusion, it needs to be thought off in pure maths terms, the only place you will ever find it.
Click to expand...

Exactly.
 
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