prove to me that 0.999... does not equal 1

>>8840612
Wouldn't that imply that .000... = 0?

>>8840612
But it does....
>>8840617
This is also true. An infinite amount of zeroes equals zero

>>8840612
Do people that constantly make these threads just have never been through calculus? Not understand convergence?

>>8840633
op here
i do believe that 0.999... = 1
but im curious to see people try to disprove it

>>8840617
>implying proof by contradiction is valid

You literally posted an algebraic proof of it as your image, don't pretend this wasn't a clickbait thread for (you)s.

Prove to me that it does without using erroneous approximations of fractions.

>>8840658
You might as well ask me to prove it using toothpicks

>>8840658
What is 0.999... + 0.111...?

>>8840678
1.1 repeating

>>8840701
What happens when you subtract 1 from that?

>>8840706
same thing as subtracting 0.999...

you get 0.111...

>a number with infinite significant figures has the same value as one with one significant figure
>people actually believe this

>>8840658

I'm going to take the bait.

1. If you accept the properties of real numbers then you are forced to accept that .999...=1. Why? Because there is no number between .999... and 1.

2. Convergence of geometric series.

3. The supremum and infimum of .999... are both 1. But this is impossible unless .999... = 1.

Fuck you. I hate the use of the word brainlet in pretty much any context, but anyone who claims that .999...!= 1 is an actual, true to life fucking brainlet.

>>8840637
You are what's wrong with /sci/. Can't we clean this board up a bit, please?

So 9.999999....=10 ?

>>8841126
9.99...=9+0.99...=9+1=10
Did you even need to ask?

>>8840612
does 999=1000?

>>8841198
No, but 999.999..=1000

Does that mean 3.1415...99999... = pi?

So the square root of .9999999999...
Equals the square root of 1?

>>8841231
>>8841251
could be on to something here

>>8840612
(1-0.99...) = 0.000..1
(1-0.99...) + (1-0.99...) = 0.00...2
0.00...2 * inf = 2

but if 0.999... == 1 then
(1-0.99...) = 0
(1-0.99...) + (1-0.99...) = 0
0.00...2 * inf = 0

>>8841256
>0.00...2 * inf = 0
should be 0 * inf = 0

>>8841116
Can we just add the fraction proof to this and make this an automated answer for these threads so we can shut them down immediately?

>>8840612
suppose [math]0.\overline{9}=1[/math]. then let [math]\epsilon>0[/math]. if [math]0.\overline{9}+\epsilon=1[/math], then [math]\epsilon=0[/math]. but [math]\epsilon>0[/math], which is a contradiction.