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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But X.0 has the same value as X.000 and so on, where as X.9 doesn't have the same value as X.999

X not being anything to do with algebra, just meaning any number.
 
Please let's not associate "philosophy" with believing that 0.9r != 1 and mathematics with 0.9r = 1. The link you posted, is someone's opinion albeit a professional mathematician/philosopher, but that doesn't make them right; there are plently of philosophers who would disagree with it.

Harley, I'm afraid in this case you might just be wrong and have misunderstood the subtle reasoning that it takes to see that 0.9r actually refers to the same concept as "1".
 
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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.
Click to expand...

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
 
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If this is a strictly mathematical question, then 0.9r does indeed = 1, but this is as much convention as anything else.

In my (philosophical) opinion the confusion is caused like this:

There are two points that exist an undetermined finite space apart from each other.

How much pure "space" is in between these points?

You would try to work this out by finding out how many times you can divide up a space (or just 'space'), and when you get to the smallest amount, you count how many "atoms" of space there are in between the two points.

You then realize that you can divide space an apparently infinite number of times

You then also realize that even an infinite amount of "space" would have no value (distance in this case) because the idea of having "units" or "atoms" of space is a non-concept

It is a mis-use of reason to attempt to find atoms of space because space is a concept required to have the concept of objects in the first place.

We can have units to measure distance between objects because the units are relative to other objects which exist in space, but you cannot measure space itself.

I believe this is the basis of the age-old confusion.

[/philosophical mode]
 
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