What's your favourite paradox?

[Divey]

This is all too complicated for me.

[mgdwszx]

I have a few;

This is just something to make one think: 0.999... (0.9 recurring) = 1. Do you agree?

Did this recently as an addition to one of the topics I'm studying:
If 0.999... = x
9.999... = 10x
10x - x  would give (9.999... - 0.999...) 9.
9x = 9 so x = 1.

You must lack some brain cells
if 1 x = 0.999, then 10 * x = 9.99
now 9.99 - 0.999 = 8.991
You could also do 9*0.999 = 8.991

Basic math really

apologies, those brain cells i'm missing were irreparably destroyed by reading things you post on these forums

[Emil]

I have a few;

This is just something to make one think: 0.999... (0.9 recurring) = 1. Do you agree?

Did this recently as an addition to one of the topics I'm studying:
If 0.999... = x
9.999... = 10x
10x - x  would give (9.999... - 0.999...) 9.
9x = 9 so x = 1.

You must lack some brain cells
if 1 x = 0.999, then 10 * x = 9.99
now 9.99 - 0.999 = 8.991
You could also do 9*0.999 = 8.991

Basic math really

apologies, those brain cells i'm missing were irreparably destroyed by reading things you post on these forums

I would like to refer you to this thread instead:
http://www.fearlessrp.net/showthread.php?tid=73359

[Greed^]

You must lack some brain cells
if 1 x = 0.999, then 10 * x = 9.99
now 9.99 - 0.999 = 8.991
You could also do 9*0.999 = 8.991

Basic math really

Indeed, he's the one lacking brain cells... I'm sure you noticed the ellipsis in his solution, see my post immediately above yours about this.

Yup

Lets take a look at what he wrote

-snip-

Did this recently as an addition to one of the topics I'm studying:
If 0.999... = x
9.999... = 10x
10x - x  would give (9.999... - 0.999...) 9.
9x = 9 so x = 1.

so he says x = 0.999, and then 10*x = 9.999, but that's wrong (obviously he means in an infinite way, but this is for calculating it in a simple way), but 10 * 0.999 is not 9.999, but 9.99, which is as I mentioned before basic math, so that's where his calculations are wrong

[aviator]

You must lack some brain cells
if 1 x = 0.999, then 10 * x = 9.99
now 9.99 - 0.999 = 8.991
You could also do 9*0.999 = 8.991

Basic math really

Indeed, he's the one lacking brain cells... I'm sure you noticed the ellipsis in his solution, see my post immediately above yours about this.

Yup

Lets take a look at what he wrote

-snip-

Did this recently as an addition to one of the topics I'm studying:
If 0.999... = x
9.999... = 10x
10x - x  would give (9.999... - 0.999...) 9.
9x = 9 so x = 1.

so he says x = 0.999, and then 10*x = 9.999, but that's wrong (obviously he means in an infinite way, but this is for calculating it in a simple way), but 10 * 0.999 is not 9.999, but 9.99, which is as I mentioned before basic math, so that's where his calculations are wrong

You are correct, but it's irrelevant to the topic at hand. 10*0.999 is obviously 9.99. That's not the computation franku is doing however. Hence, he is indeed fully correct.

[Greed^]

-snip-

Did this recently as an addition to one of the topics I'm studying:
If 0.999... = x
9.999... = 10x
10x - x  would give (9.999... - 0.999...) 9.
9x = 9 so x = 1.

eh?

[mgdwszx]

-snip-

Did this recently as an addition to one of the topics I'm studying:
If 0.999... = x
9.999... = 10x
10x - x  would give (9.999... - 0.999...) 9.
9x = 9 so x = 1.

eh?

(...) = recurring decimal
9.999... means the '9' value after the decimal place continues indefinitely (1÷9 = 0.1 recurring, for example)
So if x = 0.999 recurring, multiplying that value by ten will move one nine to the left, giving 9.999...
If you subtract 0.999 recurring from 9.999 recurring you are left with 9, hence my calculation.

edit: the recurring decimal values cancel themselves out

[Greed^]

That'd still make your calculations wrong

You can put any amount of 9's after the .... and it'd still follow the same principle that I wrote

[mgdwszx]

That'd still make your calculations wrong

You can put any amount of 9's after the .... and it'd still follow the same principle that I wrote

was going to explain all over again but honestly cba, here are some sources you should take a minute to read over:

http://www.purplemath.com/modules/howcan1.htm
https://www.math.hmc.edu/funfacts/ffiles/10012.5.shtml
https://en.wikipedia.org/wiki/0.999...
http://www.relativelyinteresting.com/doe...y-equal-1/

[aviator]

Right, here's a more visual representation of what he has done:


The last line shows 3 different ways of expressing the exact same number: 0.999..., 9/9 and 1.

Another way of expressing 0.999... or 0.9 recurring is by the following infinite (and converging sum), which is equal to 1:


The above notation effectively means: 0.9+0.09+0.009+... going on forever.

I'll show you that the above sum is true as it is a geometric series, so the sum to infinity is:

where a is the first term (in this case 0.9) and r is the common ratio (what we multiply to get the next term) which is 0.1 in this case.
When we apply the formula:

Hopefully this clears it up a bit more.