/sci/ - Science & Math

>>10362083
if more than fingers, infinite

>>10362083
Put her on blast, go viral, get her fired, win. Be the change.

>>10362083

>>I could prove that 1 = 0
Did you ask for her proof?

>>10362083
>>"And? You can prove anything in math."
> Not telling her you can prove mathematically that she's going to suck your dick

>>10362083
>>she says 0.999... ≠ 1
>I prove it
Prove it, little guy.

>>10362083
>"proving" it by symbolic manipulation and tricks manipulating an infinite string of decimals
She's not wrong, that isn't rigorous. The same techniques are used to prove 1+2+...=-1/12.

>>10362201
>>10362347
People like you will be found out and kicked out of all STEM subjects for the rest of your lives

>>10362351
Lol, I bet you couldn't actually prove it.

>>10362394
The proof is trivial

>>10362083
>You can prove anything in math
damn she is dumb

>>10362083
i’m taking calc 1 and yesterday the professor showed basic rules for finding derivatives, like cx^n derived is just (n*c)x^n-1, and so on. But here’s the thing: she said we “aren’t allowed to use these” on the test. She said if we solve a derivative using these facts, she will not give us any points for the question. I’m not experienced enough to say with certainty, but isn’t that kind of retarded?

>>10362394
x = 0.999...
10x = 9.999...
= 9 + 0.999...
= 9 + x = 10x
9 = 9x
x = 9/9
x = 1

I'm surprised I remember this

>>10362083
have her help you with baby rudin; the chapter where he defines real numbers, and then ask her about this again while keeping the page open on the definition

>>10362083
What grade was this in?

>>10362553
>10x = 9.999...
Sorry, this isn't rigorous. You might as well have written
>9.999.... x = 10,
it would make just as much sense.

>>10362589
how much is 10 times 0.999...?

>>10362589
>being this incel-cucktroll

0.999... + 0.111... = 1.000...
T H E R E F O R E
0.999... =/= 1

Shit talking her online because she rejected you? LOL.

>>10362621
yikes

>>10362621
won't it be 1.000...1 :^)

>>10362548
the entire rest of the course is solved using that she probably just wants you to demonstrate you understand what's actually going on behind just adjusting the coefficent and exponent

you do the same thing at the start of calc 2 with integrals

>>10362548
She wants you to solve using the limit process. Thankfully, my professor only had one of those questions on the test

>>10362548
you solve using the definition of a derivative for the first chapter then the rest of the class and all of calc beyond is using what you just described

>a decade of /sci/
>.99999 = 1 threads still around

Feel nostalgic man

>>10362594
He's right. 0.999... = 1 is true, but that proof isn't rigorous.

>>10362949
it is rigorous, but have another:

1/3 = 0.333...
3 * 0.333... = 0.999... = 3*(1/3) = 3/3 = 1
0.999.. = 1

>>10362949
How not?

>>10362949
Brainlet

>>10362083
0.999...=1 isn't provably true. It's true by definition. 0.999... isn't a number, it's a limit. And we say that a limit is equal to a given number when we can prove it is always arbitrarily close to that number.

>>10362953
All right you seemingly helpless baby bird, how about this:
THM: ...999 = -1
PRF:
...999 + 1
= ...990 + 10
= ...900 + 100
...
= 0

>>10362953
>1/3 = 0.333....
Not proven

>>10363178
>...999
this isn't a thing

>>10363209
> ...999 isn't a thing
Prove it, faggot.

>>10363213
>weeb
>can't math

shocking (not)

>>10362083
>retards ITT

2/0.999... = 2.0000.......00000.2
2/1 = 2

therefore 1=/=0.999...

>>10363178
I prefer this proof, following OP's style.

Proof. ...999/10=...999.9
Thus ...999/10 - ...999 = 0.9,
thus (-0.9) ...999 = 0.9
i.e. ...999 =-1

>>10363149
>0.999... isn't a number
0.9... is an integer

>>10363185
prove it

>>10363281
Okay, prove it.

>>10363286
I can imagine 1, 3, and the ratio between them (1/3). But I cannot imagine a ratio comparing infinite lengths, because I have never perceived anything that has infinite magnitude

>>10363294
>math isn't, because i'm stupid
k

>>10363288
0.9... = 1
1 is an integer

>>10363305
Yeah, that's what I thought. All talk and a badge.

>>10363311
that's what she said

>>10363301
Math doesn’t require the concept of infinity to work in the real world

>>10363115
0.9999... being some element in R and 1 being an element in R. lets call them x and y, because R is convex ax+(1-a)y=z exists and is an element in R for 1>a>0. Now if we take a look at x and y there exists no such z therefore x=y is proven by contradiction.

Especially the 1/3 prove is utter bullshit. You can't just prove something is true by assuming it is true ie.: stating 1/3=0.333...

>>10362631
Yes, I'm a brainlet.

>>10362083

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

>>10362621
wrong, 0.9999... + 0.00...1 = 1

>>10362953
1/3 = 0.3333... + (remainder) 0.000...1/3
1/3 * 3 = 0.9999...9 + 0.0000...1

[math]x = .9999...[/math]
[math]x = \frac{9}{10} + \frac{9}{10^2} + \frac{9}{10^3} + ...[/math]
[math]x = \frac{9}{10} + \frac{1}{10}(\frac{9}{10} + \frac{9}{10^2} + ...)[/math]
[math]x = \frac{9}{10} + \frac{1}{10}x[/math]
[math]x - \frac{1}{10}x = \frac{9}{10}[/math]
[math]x(1 - \frac{1}{10}) = \frac{9}{10}[/math]
[math]x(\frac{9}{10}) = \frac{9}{10}[/math]
x = 1

>>10362183
x^2 = x*x = x+x+x....x+x (x times)
take derivative of both sides:
2x=1+1+1...1+1 (x times)
2x=x
2=1
1=0

>>10363557
2x = x is only true if x = 0 so you can't divide both sides by 0, it's not a number

>why this boards still allow niggers to participate?

>>10363557
>0^2 = 0*0
>1 = 0

>>10363553
>x = 0.999...
This was your first mistake. A variable cannot be made equal to an infinite sum, because the former has a fixed value while the latter does not.

>>10362548
Holy shit. Is that how math looks like in American universities? Derivatives?

>>10363565
the whole point of the "proof" is to show that 2x=x for any x

>>10363592
but it's not, that's why you niggers fails school

>>10363597
>the proof is wrong
yes, good job. 1 = 0 is in fact wrong. Absolute genius.

>>10363629
Is it because the rhs is taking the derivative of constants?
t. brainlet

im having alot of fun guys.

>>10363637
>>10363629
again: stupid people repeating the obvious in this board
>inb4 bolzano strikes back

>>10363557
Very cool, took me a while to figure out. If I understand correctly, this is because x^2 is a function (over let's say the integers) while x+x+...+x (x times) is NOT a function, but some kind of construction that gives us a specific function for each x. Some kind of generator.

Let's say that G(n) is the generator in question; G(n) is a function from the integers to the functions on integers. For example, G(3) gives us the function x+x+x, while G(2) gives us x+x. In other words, G(n) is the function n*x.

NOW, we see that the asserted equality, x^2=x+x+...+x (x times) i.e. x^2=G(x) for all x, makes no sense because how could G(x) be equal to x^2 for all x? Just as an example, let's take x=5. Then x^2 is just 25 while G(x)=G(5) is the function 5x, which is definitely not equal to 25.

by defintion [math]0.999\dots = \sum\limits_{n=1}^{inf}9\times 10^{-n} = 9\times\frac{10^{-1}}{1-\frac{1}{10}} = 1[/math]. u can't argue with that. And yes it converges because 1/10 < 1

>>10363657
>while x+x+...+x (x times) is NOT a function
is not a function from the same domain and with the same codomain as x^2, I should have said.

>>10363670
>implying ∞ is a number and not a concept

>>10363450
...999 being some element of R, we can conclude that ...999=-1. Engage with the argument >>10363226 or admit you're a dumb faggot.

>>10363677
Reply or mom die
ok

>>10363677

No. When it exists [math]\sum\limits_{n=0}^{inf}a_n = \lim\limits_{N->\inf} \sum\limits_{n=0}^{N}a_n[/math]. infinity isn't a number here

>>10363691
>>10363686
buttblasted

>>10363697
make the sum step by step from 0 to infinity in a paper an tell me when you finish it, niggerjew

>>10363677
>>10363699
dubsblasted

>>10363705
write 0.9999....
this hole thread is about the concept of infinity.

>>10363714
your stupidity reaches for sure the infinite

>>10363705
yeah of course, that's how math works

>>10363697
The use of the concept infinity only means that we can get arbitrarily close to the limit. We can keep summing to get closer to that limit. The sum doesn’t actually exist as a fixed value. Never has any mathematician proved that you could actually take an infinite sum. It’s merely an assumption, and everyone ITT is using this assumption in their “proof.” If something is infinite, it can never be completed.

>>10363722
That is how math works. Every human use of mathematics would work just as easily if we discarded the erroneous idea that infinity exists, or that infinite sums exist, or that space is continuous, etc.

take your age, add it 10, then substract it 5 and then substract it 5 again. and you get your age again

take the current year, substract it your age and you'll get the year you were born

pick a number between 1 and 1000, multiply it by the number of functional neurons you have. The result is 0.

>>10363725
[math]\sum\limits_{n=0}^{inf}9\times10{-n}[\math] isn't a sum. it is a limit of a sum which is a number which is 1

>>10363725
>If something is infinite, it can never be completed.
Same happens with your mom's vagina or the amount of horse cum you swallow on a daily basics

>>10363731
inifinity is just a fucking definition in the case of real sequences

>>10363746
my sides are in an infinite horbit, gigakek

>>10363746
Not an argument. How does it feel knowing math would be perfectly fine without the invention of infinity?

>>10363751
remember when people was being murdered because they proposed the square root of negative numbers?

>actual, legitimate retards ITT comparing a divergent sum (1 + 2 + 3 + 4 + ...) to an absolutely convergent sum (0.999...) and saying that assigning a finite value to one is as valid as assigning a finite value to the other
Did you even fucking pass Pre-Calculus?
Get the fuck off my board.

>>10363557
If you say that x^2 equals x+x+...+x (x times), then you implicitly say that x^2 as a function, in this particular context, has as its domain the positive integers. However you can't take a derivative of a function at a point that is not an accumulation point. Since the integers does not have any accumulation points, you can't take the derivative of x^2 meaningfully in this context. Thus your second step is erroneous.

>>10363677
Silly.

>>10362083
>I could prove that 1 = 0. That doesn't mean it's true
If she could, it would, that's why she can't.
Holy crap anon, time to meet with gurls older than 7

>>10362621
>she rejected you
>>10364319
>time to meet with gurls older than 7
Learn reading comprehension, Anons. This was OP's math teacher, someone with a license to educate people on mathematics, and she didn't even know basic calculus.
Why would anyone make a thread just about some girl being dumb? Why would anyone think anybody else was interested in reading that?

>>10363219
He's right, you are supposed to prove it by showing the two sequences converge. That is how equality of real numbers is defined. You are doing baby "proofs" that only exist to help with intuition and acting all smug about it.

>>10364346
>it's his maths teacher
that makes it even worse

>>10364390
You could also prove two reals equal by proving their difference smaller than any positive rational.

>>10363557
>x^2 = x*x = x+x+x....x+x (x times)
ok what if x = 2.3, type it out please

>>10363670
Using analysis to prove repeating decimals are equal to whole numbers is like pulling yourself up by your own bootstraps. It presupposes what you are supposed to prove.
Protip: you can't.
Bonus: irrationals do not exist.

>>10362347
>prove 1+2+...=-1/12
Except no mathematician outside of numberphile ever claimed that was true

>>10365825
Yeah, it's not true. It's just a result of bad arithmetic.

>>10363541
This.
And since 0.999... =/= 0.999... + 0.00...01
then 0.999 can't equal 1.

>>10363541
There is no such thing as 0.000...1 you fucking moron
>>10365862
You are a moron

>>10365792
>Bonus: irrationals do not exist.
another moron is found.

>>10365862
>0.999... =/= 0.999... + 0.00...01
1 = 1 + 0

>>10362083
>female professor
you asked for it

Imagine being so stupid you genuinely can't understand the reals

>>10363149
Wrong. 0.999... is a number. The sum of 1/10^n approaches both 0.999... and 1, thus they are equal.

>>10365929
>the graph 1/x approached zero, therefore it will touch the x-axis

>>10365869
There is no such thing as 0.00.....1 but the point stands: something must be added for a 9 to become a 1. How can the 9’s magically become 1? Every step, they are only 9/10 of the way to their destination. The gap is never closed. It never equals 1.

>>10365878
You'll never be able to establish their existence. You can presume they do, but that's not proof.

>>10365825
>what is the Riemann zeta function evaluated at -1

>>10365936
Wow you're dumb. The point is not that a function reaches 1, the point is that it approach both 0.999... and 1. Since it can't approach two different limits they are equal.

>>10365967
There is no final step, so your point is moot.

>>10366007
>LALALA asymptotes are never touched but 0.999... equals 1 LALALA
>>10366013
You’re right, the sum never ends, it is never completed, and it never equals 1. There is no such thing as “at infinity” or an infinite sum existing. Infinite means without end. 0.999... isn’t a fixed value.

>>10366032
0.999... = 1

>>10362347
>>10365825
>>10365833
The worst part is that [math]1 + 2 + 3 + 4 + \dots = -\frac{1}{12}[/math] actually is true... if you, as those who originally drew this conclusion, define [math]=[/math] to mean "is associated with," and it can indeed be proven that that series "is associated with" [math]-\frac{1}{12}[/math] through actually rigorous methods (zeta regularization, integration, etc.).
The thing is, of course, that nobody uses that notation like that, so you get pop-sci/pop-math retards like Numberphile and their audience who read that Ramanujan wrote [math]1 + 2 + 3 + 4 + \dots = -\frac{1}{12}[/math], assume that he actually meant that the divergent infinite series of natural numbers sums to a finite negative fraction, and unquestioningly accept it because they are retards to whom math is indistinguishable from wizard magic.
And the "proofs" they use to justify this "sum" absolutely are unrigorous; you actually can algebraically manipulate an absolutely convergent series term-by-term (for instance, you can fiddle with the infinite series of [math]\exp{\left(x \right)}[/math], [math]\sin{\left(x \right)}[/math], and [math]\cos{\left(x \right)}[/math] to prove that [math]\exp{\left( ix \right)} = \cos{\left( x \right)} + i\sin{\left(x \right)}[/math] because those are all absolutely convergent), but you definitely cannot do that to a series that is anything less than absolutely convergent—at least, you cannot do that and expect to get an actual sum—and you especially cannot do that to a series that is demonstrably and obviously divergent like [math]1 + 2 + 3 + 4 + \dots[/math].
...That said, this does mean you can algebraically manipulate [math]0.999 \dots[/math] like that, since it is absolutely convergent (to [math]1[/math]).
But you can't use that to prove that.

I'd hope that this would end all the retarded comparisons to [math]1 + 2 + 3 + 4 + \dots = -\frac{1}{12}[/math] ITT, but I've learned all too well that there is no stopping retards.

>>10366032
>LALALA asymptotes are never touched but 0.999... equals 1 LALALA
Asymptote of what?

>You’re right, the sum never ends, it is never completed, and it never equals 1.
The infinite sum is equal to 1.

>There is no such thing as “at infinity” or an infinite sum existing.
They do by definition.

>Infinite means without end. 0.999... isn’t a fixed value.
One has nothing to do with the other.

>>10362183
Her "proof" would probably have been something retarded like:
[math]
a = b \\
a^2 = ab \\
a^2 - b^2 = ab - b^2 \\
(a + b)(a - b) = b(a - b) \\
a + b = b \\
a + a = a \\
2a = a \\
2 = 1 \\
1 = 0 \square[/math]
The funny thing is that I bet you none of the [math]0.999\dots \neq 1 [/math] retards ITT can tell you what's wrong with this... which unfortunately makes them qualified to teach mathematics in the United States.

>>10367361
Can’t divide by zero. Now tell me how 0.999.... = 1 contributes to mathematics and why it’s necessary to know.

>>10362201
1/3 = 0.333...
1/3 + 1/3 + 1/3 = 1
0.333... + 0.333... + 0.333... = 1

>>10367373
>Now tell me how 0.999.... = 1 contributes to mathematics and why it’s necessary to know.
You are moving the goalposts and therefore not arguing in good faith, and I refuse to continue a conversation with someone who is not arguing in good faith. Good day.

>>10367373
This particular fact is in itself not very useful, but it follows from the interesting tature of convergent cauchy sequences of rationals and how they are used to define the reals (namely as the limits of these sequences).

>>10362621

>>10362201
https://en.wikipedia.org/wiki/0.999...#Infinite_series_and_sequences

>>10365967
0.9999... is defined as the limit of the sequence 0.9, 0.99, 0.999, 0.9999... which is 1 you idiot

>>10365825
>>10366544
It's true you idiots.

>>10367536
>The worst part is that [math]1 + 2 + 3 + 4 + \dots = -\frac{1}{12}[/math] actually is true
Literally in the second post you quoted, brainlet.

>>10362347
[math]1+2+3+\dots=-\frac{1}{12}[/math] is literally true, just like [math]1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\dots=\frac{\pi}{4}[/math] is literally true. There's no good reason to say otherwise. We've had this discussion before: >>/sci/thread/S10294026..

>>10367542
For the second post I meant the whole bullshit about "being associated with". No one qualifies the equal sign in other contexts where summation is generalized from naturals, to integers, to rationals, to reals, to limits of partial sums, etc.

>>10367552
That's literally what the equals sign means in that context, though. You're right that it's bullshit, though, and I'd argue that it verges on deceitful abuse of notation.

Wildberger was right, fuck all these smug faggots