Why is this allowed?

>I can't into infinity
Poor b8

[math] \displaystyle
1 = \frac {3}{3} = 3 \cdot \frac {1}{3} = 3 \cdot 0.333... = 0.999...
[/math]

[math] \displaystyle
3 \cdot 0.\overline{3} = 0.\overline{9} = 0.1_3 + 0.1_3 + 0.1_3 = 1_3 = 1
[/math]

>>8401830
Because infinite repeating decimals are just a silly notation for geometric series.

[math]0.99999... = \sum_{n=1}^{\infty} \frac{9}{10^{n}} = \left \sum_{n=0}^{\infty} \frac{1}{10^{n}} \cdot 9 \right - 9 = \frac{9}{1 - \frac{1}{10}} - 9 = 1[/math]

>>8401830
The last is just 1 since the decimal value is infinitely close to 1

>>8401830
You forgot to carry over the 1 from the end :^)

>>8401864
Fuck this shit.

[eqn]0.99999... = \sum_{n=1}^{\infty} \frac{9}{10^{n}} = \left( \sum_{n=0}^{\infty} \frac{1}{10^{n}} \cdot 9 \right) - 9 = \frac{9}{1 - \frac{1}{10}} - 9 = 1[/eqn]

>>8401864
>silly notation
aaaahahahaaaaaaaa

>he doesn't use base 12

>>8401830
Because people don't like accepting that math is wrong.

>>8401935
It will still happen with other numbers

decimal numbers bro

.999999... = 1 bro

>>8402078
.9 is not 1.

>>8402082
.9999999999999.... not .9
Is this bait? Are you a precalc student?
Learn some about infinity. Learn some about maths.

Geometric series thread stale bait is stale

>>8401830
because you touch yourself at night.

>>8402170
I touch myself during the day.
I'm touching myself right now.

>>8402155
It doesnt matter how many 9's you have, at no point does a .1/.001/etc ever appear, .9.. will never be 1.

>>8402189
https://en.wikipedia.org/wiki/0.999...

>>8402194
>wikipedia
May as well link some christian loony website that says the earth is only 6k years old

>>8402194
an infinite .9 is not 1, you cant just pretend its 1 for convenience, thats not how it works.

>>8402212
>christian loony websites cite academic sources

10x=9.999.....
x=0.999....
10x-x=9.999....-0.999....
9x=9
x=1
1=0.999....

>>8401830
glitch in the matrix

>>8402340
```shiiiiiiiiiiiiiiiiiiid```

Don't mind me. I'm trying to figure out how to Latex on here.

Sometimes everything is in that shitty box. But other times, it actually looks nice.

For example, I think this puts in that shitty box.

[math]
\frac{\partial }{\partial x}H\left(x\right)+\frac{\partial ^2}{\partial x^2}T\left(x\right)=\sum _{i=1}^N\left(\sqrt{x_i}\right)
[/math]

>>8402189
>>8402212
>second year engineering students think they know some shit about math after taking calc 1.5

File: proof.png (627KB, 730x2824px) Image search: [Google]

627KB, 730x2824px

>>8402212
Since you insist, here is a rigorous proof.

Enjoy.

For fuck's sake, are you guys adding/substracting infinitely long decimal numbers again? Here's your daily reminder that you don't need to do that nonsense, just use the following:
>Two real numbers x and y and equal if and only if there does not exist another real number z such that x < z < y.
Bam, you're done - there is no number between 0.9... and 1.0...

>>8403413
Whoa, i mean i have done it algebraically but that is some next level shit. Mostly because it is so simple.

>>8403413
But what if I have infinitesimals?

>>8403428
"Infinitesimals" and "infinities" are not to be confused with numbers.

>>8403428
Go ahead and define a number system that includes infinitesimals, while maintaining all the nice properties of the reals.

>>8403435
>>8403440
Hyperreals.

>>8403442
This is a real analysis problem, not a hyperreal analysis one. I'm sure you could come up with your own construction where 0.9... != 1.0... but I doubt you would find it to be useful for the purpose of real analysis.

>>8403455
The transfer principle still holds for the hyperreals.

>>8403462
Well you just proved the point then, didn't you?
>"The transfer principle states that true first order statements about R are also valid in *R."
The statement
>Two real numbers x and y and equal if and only if there does not exist another real number z such that x < z < y.
can be written as a first order statement and is true in R. Hence it's also valid in *R.

How can I profit from 0.9999... = 1?

Office Space made fun of it but there would certainly be something to it with large volume transactions

>>8402189
>engineers
why do we let you brainlets post on our board?

>>8403420
When you finally graduate high school and start university, that's when you start learning real maths.

>>8401830
because math works.

>>8403390
in line 16, where he says "a n", does he mean the same "a n" that is visible in line 15, or does that mean any a of all shown? and what does n > 0 mean?

>>8403413
Since youre just working with infinity, im just gonna work with infinity too.

z = 0.9.. + (1 - 0.9..)

bam. theres a number larger than 0.9.. and smaller than 1.0..

>>8404515
But it just says 1+1-1 = 1+0 = 1

>>8404515
I hope this is a joke.
Suppose x and y are different numbers.
Then x + (y - x) = y.
Suppose x and y are the same number.
Then x + (y - x) = x.

>>8401830
Is there any residual effect on the economy or do they not deal in fractions?

>>8404516
no it doesnt.. you didnt use infinity. you gotta use infinity to make sense.

>>8404519
and whats your point again? all you did was take the lower number and add the difference between lower and higher number to get higher number

>>8404526
You're fucking dense.
You put forth a method whereby one could obtain, using two numbers, a third number which is different from the original two. However, your method was flawed, and I exposed that flaw in >>8404519 by showing you that by your method, in all cases, one could not obtain a third number which is different from the orignal two.
That was my point.

>>8404539
Again.... Your example doesn't work because you aren't using infinity

>>8404558
Oh I see, I think you're in the wrong place;
>>>\b\
is that way.
In the event you're trying to be serious, please see >>8403462.

>>8404567
>>>>\b\
Nice argument man.

I dont know what "transfer princizple" or "hyperreals" mean

>>8404570
http://lmgtfy.com/?q=Hyperreals

>>8404586
what do i get for googling false informations?

>>8404505
He's talking about any a.

>and what does n > 0 mean?
He's saying that only the numbers with n > 0 have to be between 0 and 9.
Since a_0 can be any number, as it is the non-decimal part of the number (however on the previous sentence he restrains it for the positive integers only).

In short: a_0 any positive integer, any other a_n with n > 0 has to have a value [math]0 \leq a_n \leq 9[/math]

>>8402189
So, what's 1-0.99999…

>>8403539
Weren't they talking about floating point numbers? 1/3 is non terminal.

>>8401935
>thinking base 12 is better than base 6
base 12 plebs really grind my gears

File: 1475651368148.jpg (174KB, 640x640px) Image search: [Google]

174KB, 640x640px

Geometric Series are a bitch so far to me
I can understand that to get r you need to divide one term by the one before it. But where the heck does a come from?
Like in [-1/2, 1/4, -1/8, 1/16...] all I can figure out is r but I can't do jack shit after that. What's a good online resource to learn this shit? My professor refuses to explain how to get the 'a' in 1/(1-r)

>>8405063
The a is just the initial term of the series

as in, if your series is
1, 1/2, 1/4, 1/8...
a is 1
if your series is
1/3, 1/9, 1/27...
then it's 1/3

>>8401830
i actually don't get what the deal is with this, 0.9 is not 1.
so what the fuck? we can't accelerate a particles speed to 0.9 times the speed of light, but that is just close to the speed of light, not the speed of light

>>8405841
0.9 is not 0.99999....