/sci/ - Science & Math

>>9717619
Would you mind demonstrating that? I mean with a physical demonstration, like take an apple and divide it into zero parts

>>9717622
Suppose we have a group of 10 coins, and we divide it into zero groups.

How many objects are in each group? Zero.

>>9717627
Would you mind drawing a picture?

>>9717627
In this example you assume that there is at least one group with # of elements = 0. First, you would then at least have ONE group and second it isn't really consistent, since saying sth. Like "divide into zero groups" does not make sense whatsoever yet alone the concept of size inside a non existent group.

>>9717632

>>9717639
In a dashed group the concept of elements inside that group makes no sense

>>9717639
Those objects are still there and as they're the only relevant parameter the group that does not contain them isn't a group, it's an antigroup

So 5/0 = 5?

>>9717627
>we divide [it] into zero groups
So you have no "groups", therefore
no division has been performed.

>>9717619
WILL EVERYONE PLEASE STOP FEEDING THE TROLLS!!
On the 0/0 chance they're not a troll, they're too stupid to be convinced.

>>9717788
Technically there's a 50% chance they aren't a troll

>>9717804
No, statistics are not binary, you troll

>>9717619
Take the function 1/x

At 1/1 = 1
1/.1 = 10
1/.01 = 100
.
.
1/.00000001 = 100000000
Until you reach Infiniti as you approach 0.
Infinity in that sense isn't actually a number. It's theoretical. You could never do it, make it, go it, wtvr.

But get this
1/-1 = -1
.
.
1/-.00000001 = -10000000
Until you reach - infinity as you approach 0.

So tell us, at 0, what should x be? Every number from negative infinity to positive infinity as it crosses the y axis at 0?
Professional mathematicians just prefer to call it "undefined" because you can't do it. 1/x doesn't exist at 0.

>>9717804
If "troll" is only 50% probable, then "stupid" is also 50%.
Giving a 100% probability that arguing is a waste of time.
YOUR time.
I don't care about theirs.

>>9717639
That just looks like you got cut out of the deal and someone else got all 4 apples.
They didn't disappear, offsetting the entropy of the cosmos. They still exist. It actually just looks like you didn't devide them at all, you just have an empty shopping basket.

>>9717838
Kek, based response

>>9717619
How many zeros, lumped together, equal 5?

>>9717842
Its almost like Wildberger was right.

>>9717838
You're forgetting that there is also a 50% chance they are right

>>9717619
0 isn't a real number, it just behaves like one sometimes. trying to divide by zero is like trying to get to nowhere

>>9717619
How many times can we subtract 0 from 5 before we reach 0 ?

(5 - a*0 = 0), what is a?

>>9717885
??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????0 is in R ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

>>9717885
OP is retarded but 0 is in R lol

>>9717619
>Let's take 5 divided by zero. That's obviously equal to 0
So what happened to the 5?
Division is not subtraction.

>>9717627
So what you are saying is that you haven't divided.
You haven't even divided into one group. You said "Let's divide these coins into zero groups" and then tossed the coins over your shoulder and walked away.

Division by zero makes no logical sense because if you have a group to begin with and you end up with any number of groups then you haven't divided by zero.

>>9717619
>that's obviously equal to 0
Calculate quick the limit of y as x-> 0 for y=5/x and tell me its obviously 0

Explain it to me like I'm fucking dumb because I am /sci/

HOW DOES MODULUS WORK WITH NEGATIVES?

I always thought of modulus as a remainder operator i.e. 5 % 10 would be 5 because 5/10 in integer division is 0 with a remainder 5. 5 % would be 2 because 3 goes into 5 once with a remainder of 2 etc. etc.

When it comes to negatives I get completely lost.
-5 % 3 in my mind would give -2, but it gives 1.

-3 % 7 in my mind would give -3 for the above reason but it's instead 4. The only way I can wrap my head around it is if I just subtract the first from the second, if the second is larger and the first is negative, but I KNOW this isn't how it works.

I came across this problem while looking at a solution for simplifying a rock paper scissors script in python using dictionaries and keys.

I didn't understand how or why modulus could be used to eliminate all the conditionals and relegate it to one line to determine whether user input won.

tl:dr How does modulus actually work with negative numbers? I can't understand the actual reason, even though I know a brain dead solution.

is everyone here pretending to be retarded?

>>9717627
dividing 10 objects into zero groups of zero. There is no group to begin with, so you can't have zero coins in each group.

>>9717619
>dividing by 0
OP is either retarded or Chuck Norris

>>9717619
Because majority of people are either more intelligent than you or less ignorant.

>>9717627
>Suppose we have a group of 10 coins, and we divide it into zero groups.

But if you're allowed not to put the ten coins in your group, couldn't you have two groups of zero coins? Or ten? Or an infinite set of groups?

>>9717845
Yes, 0*X=5 has no solution. But that doesn't mean 5/0 doesn't. It does, and it's infinity.

Infinity is very inconvenient to work with (seeing as it isn't a number) and a division that doesn't have a multiplication as its inverse is also very inconvenient. For these reasons, mathematicians often prefer to say "fuck it. We'll just avoid doing it, because it's not worth the trouble".

And I agree, it really isn't worth the trouble. But that doesn't mean it doesn't exist or doesn't make sense. It does and it does.

ya if x/0 was defined R wouldn't even be a vector space which would be funny af famalam

>>9717619
>since 5 * 0 equals zero.
Haven't read the thread yet, and I'm drinking Tequila at work but here goes:
If 5*0 = 0, then...
0/0 = 5
and
0/5 = 0

Convince me I'm wrong.

>>9717639
"dashed lines represent a lack of a group"

>>9717814
>No, statistics are not binary, you troll
I'm going for a walk.
I'll either get hit by lightning, or I won't
50-50 bruh.

>>9718059

>>9717639
>We can divide by zero if we don't actually DIVIDE anything
Retard.

>>9717838
Probability isn't a percentage you orangutan.

>>9717619
>>9717627
>>9717639
the reason is mainly theoretical in nature
if you allow division by zero you can basically proof everything
this video might be very simple and for kids but it gets the point across perfectly
https://www.youtube.com/watch?v=hI9CaQD7P6I

>>9717619
If A/B = C,
Then C*B = A.
You propose 5/0 = 0.
Then you are also proposing 0 * 0 = 5.
Yet 0 * 0 is clearly 0, therefore 0 * 0 = 5 is false and so 5/0 = 0 is also false.

You can instead of dividing, multiply by the inverse. So 5/0 =5*1/0=5*1*1/0...
Then you open that so there's no space to post the real answer.

>>9717788
>tfw /sci/ is too retarded to get the 0/0 joke

This is the spookiest thread I've seen in a while.

>>9717622
>taking the kindergarten definition of division literally

>>9717831
>implying functions have to be continuous

>>9717845
>>9718105
>>9718566
>implying all operations are invertible

>>9717891
>implying division is repeated subtraction

>>9718600
I was actually trying to figure out how often something happening zero out of zero times would occur

Any number divided by zero is infinity.
12 ÷ 4 = 3
>12 - 4 = 8 (1)
>8 - 4 = 4 (2)
>4 - 4 = 0 (3)

3÷3 = 1
>3 - 3 = 0 (1)

3÷2 = 1.5
>3 - 2 = 1 (1)
>[10] - 2 = 0.8 (0.1)
>[8] - 2 = 0.6 (0.2)
>[6] - 2 = 0.4 (0.3)
>[4] - 2 = 0.2 (0.4)
>[2] - 2 = 0.0 (0.5)

3÷0 =
>3 - 0 = 3 (1)
>3 - 0 = 3 (2)
>3 - 0 = 3 (3)
>3 - 0 = 3 (4)
>3 - 0 = 3 (5)
>...
>3 - 0 = 3 (34059)
>...
>3 - 0 = 3 (infinity)

it is undefined because infinity is not really number and it can't be reconstructed from multiplication
12÷3 = 4, but then 3×4 = 12
12÷0 = infinfity, but 0×infinity would then be equal to any and every number.

>>9718677
This is also why [math]\sum_{n=1}^{\infty} \frac{1}{2^n}[/math] cannot equal 1, as [math]\frac{1}{\infty}[/math] at n=infinity would equal 0, but infinite 0's would equal any number. The sum can "appear" very close to 1 by ignoring that infinite decimal places musy be filled, but it will never properly land on 1 in realtime, as well as infinitely surpassing 1 in an arbitrary time scenario where n=infinity is actually reachable.

>>9718701
[math]0.\bar{9} \neq 1[/math] for the same exact reason [math]0.\bar{3}[/math] doesn't equal any other number but [math]0.\bar{3}[/math].
Repeating decimals are unique identities unequatable to real numbers because they carry an aspect of infinity, where infinity is itself a unique identity unrelateable to real numbers where; -googol, 0, and +googol, or any number are all the same equal distance away from infinity

Holy fuck people.

Division by an x is defined as a multiplication by the inverse of x.

The inverse of x is defined as y such that x*y=1.

But, if x=0 then x*y = x*0 = 0 for any y. So there is no inverse for 0.

That's why division is not defined for 0. It's a matter of definitions. Feel free to define your own way multiplication, but then you probably can't use a lot of the math we have proven so far.

*own way of division

>>9718729
based & redpilled

>>9717619

five divided by zero isn't five?


I have five apples and I don't divide them so i'm left with five apples. Right? How is this wrong?

>>9718729
>inverse of
>t. did not attend highschool

Look at a tan graph, you can't actually divide by 0, only divide by the closest number possible. This is shown by the asymptote on a tan graph. The closer the tan 90 you get, the closer to infinity you get. You can reasonably, albeit without concrete proof conclude that x/0 = ∞

>>9718607
Math that can't be used for physics isn't real math.

>>9718677
This. It is agreed upon scientific fact.

>>9718677
Any number divided by itself is equal to 1.
Any number divided by zero is infinity.
0/0.

>>9717639
the post that ended /sci/

>>9718866
>implying all math used for physics is based purely on invertible, continuous operations

>>9718903
No, my implication was that the kindergarten definition of division is the only useful one. Wheel theory is a shitpost though.

>>9717619
that's 0 divided by 5, retard.

>>9718932
Dismiss yourself.

>>9718883
zero divided by any number is 0
0 ÷ 1 = 0
0 ÷ 2 = 0
0 ÷ 3 = 0

Any number divided by zero is infinity
3 ÷ 0 = ∞
2 ÷ 0 = ∞
1 ÷ 0 = ∞

therefore 0 is the inverse compliment of infinity, and 0 by itself must then not really be a real number just like infinity isn't, which is a fair say because most systems are designed to count the presence of something, not the absence of something.

0 ÷ 0 = [math]\stackrel{0}{\stackrel{+}{-}\infty}[/math]

>>9719211
[math]\stackrel{+}{-}\stackrel{0}{\infty}[/math]

>>9717845
>How many zeros, lumped together, equal 5?

Pretty easy.

If
[math] y * x = z [/math]

then
[math] x= z/y [/math]


We can apply this theorem in your case as well.

Since
[math] 5 * 0 = 0[/math]
This must mean

[math] 5 = 0/0[/math]

>>9717953

The Limit of f(x) is not necessarily equal to f(x)

Not all functions are continous.

>>9718872
4/0 is infinity
153523/0 is infinity
so 4 = 153523?

>>9718729
"""proven""" math of today will be rejected in a couple of centuries as retardation

>>9718607
The limits example has nothing to do with continuity in this case, you're retarded and probably failed calculus.

>>9718714
https://en.wikipedia.org/wiki/0.999......
You're a retard, please don't talk about math you don't understand.

>>9718714
>>9718701
Ffs search for "geometric series" on wikipedia.

[math] \displaystyle \lim_{n \rightarrow \infty} \frac{1}{2^n} = 0 [/math] you absolute retards.

I wont post this demonstration again. [eqn] \displaystile \sum_{n = 1}^\infty ar^n = \frac{1}{1 - r} [/eqn] and because [math] \displaystyle \sum_{n = k}^\infty a_n = \sum_{n = 0}^\infty - \sum_{n = 0}^k a_n [/math] so it follows fucking obviosly that: [eqn]\displaystyle \sum_{n = 1}^\infty ar^n = \frac{ar}{1 - r} [/eqn] so in the. Case of [math] 0.9999 \dots [/math] you have that: [eqn] \displaystyle \sum_{n = 1}^\infty 9\bigg(\frac{1}{10}\bigg) = 0.9 + 0.09 + 0.009 \dots = \frac{ar}{1 - r} = \frac{9\bigg(\frac{1}{10}\bigg)}{1 - \frac{1}{10}} [/eqn]
Motherfucking [math] Q.E.D [/math] you fucking ape-brained retards.

>>9720868
I hate posting on my phone. For the last sum its: [eqn] \displaystyle \sum_{n = 1}^\infty 9\bigg(\frac{1}{10}\bigg)^n [/eqn]
You get the idea you fucking faggots.

>>9717788
How can there be a chance of not being a troll if it is 0/0? Doesn't exist/Doesn't exist equals to one, which means you are a faggot.

>>9718105
5=0/0=6
5=6

>>9718883
0/0 in indeterminate and can have any value from -inf to 0 to +inf

>>9717619
You can't divide by zero, I suggest learning basic division if you still think you can't divide by 0 after this thread.

>>9717619
You need to define zero first.

I agree it is odd that mathematics being totally abstract work of imagination mandates that you "can't" do something. If you can do ramanujan summation and add 1+2+3+.... and get -1/12 then you sure as hell should be allowed to divide by zero. Just bend the definitions as mathematicians always do and problem solved.

>>9721402
>ramanujan summation
That shit is literally executed wrong though, that's why you get a completely nonsensical answer like -1/12. It's just a pop-sci meme at this point.

>>9721436
source?

there are plenty of videos explaining Ramanujan summation/analytic continuation. the popsci meme is high school aged redditors telling their friends that the actual sum is -1/12 which is not what is being claimed

>>9721481
Can't find the video I watched but this one explains basically the same
https://www.youtube.com/watch?v=YuIIjLr6vUA

>>9721490
yeah unfortunately I’ve already spent a lot of time watching that video. the series is not convergent, and it definitely doesn’t converge to -1/12 but it does using analytic continuation. so I’m not sure if you’re agreeing with me or not.

>>9717619
>Let's take 5 divided by zero. That's obviously equal to 0, since 5 * 0 equals zero.
I say it's infinity since [eqn]\lim_{x\rightarrow 0}\frac{5}{x} = \infty[/eqn]

>>9720868
>>9720871
Fuck off retard.
Rewriting the problem doesn't change the problem.
In your retard world you would have [math]\sum_{n=1}^{\infty} \frac{x}{(x+1)} = 1 [/math] for any integer x. First you ignore the fundamentals of existence and spacetime itself by ignoring the entire concept of rate of change, then you fuck up more by pretending infinity is anything but a non-numerical vaguely defined directive only equivalent to a verb.

>>9718701
> sum can "appear" very close to 1 by ignoring that infinite decimal places must be filled

not actually understanding this part of the post is where your concave skull mislead you.

>>9721375
-infinity and +infinity are misattributing infinity as an element relateable to actual numbers. The integer difference between -infinity and +infinity is the same as the difference between a googolplex and +infinity, if you treat it like a number. The point of infinity is that it is unreachable, so no number is any closer to infinity than any other number. -googolplex and +googolplex are still the same distance from +infinity.

infinity is for brainlets. dividing by zero gives you indeterminable work, aka infinity, aka "infinity" = "indeterminable"

Indeterminable isn't a number. Its not a value. Its not a noun. [math]0.\overline{9}[/math] has an indeterminable amount of 9's after it.
It's obviously not 1.0

>>9718701
>in realtime
Numbers not only have timestamps, but also have mustaches and sombreros.

>fuck off idiot

>>9721509
but it isn't

>>9721700
Even a retarded fucking sombrero wearing beaner would have made more of an effort to read the post than you did.

Suicide is your only way out, queer.

>>9717619
The cancellation law says if ac=bc, then a=b, provided c is not equal to zero, because for example, the expression 1x0=2x0, canceling 0 would mean 1=2 which is clearly false.

it becomes clear why you can't do it when you rearrange the formula

5 / 0 = a

a * 0 = 5
^
there is no way to solve this.

>>9721707
>I have no argument

>>9720246
The argument "the limit as x goes to 0 of 1/x is undefined, therefore 1/x must also be undefined at x = 0" only works if you presuppose that 1/x is continuous on its domain. Otherwise the limits are irrelevant to the actual values of the function and you can define 1/0 = 2 or 1/0 = 0 or whatever else you want.

>>9721901
oh shit i never thought of it like that thanks anon

>>9721680
Are fucking retarded or just trolling?
Why do you define a summation of n terms in terms of x? Have you even taken a calculus class in your misserable life?
>Infinity is anything but a non-numerical vaguely defined directive only equivalent to a verb
Im -fucking- plying.
Ill make this very simple for you, you fucking lard brained worm;
The fact that you dont understand what infinity means does fucking not mean infinity is "anything but a non-numerical..."
What the fuck do you even think are "the fundamentals of existence and space-time"?
For fucks sake you should be IP banned.
Ive said this before and ill say it again and it should be an axiom of this site so ill say it in formal verbatim;

"He who has not, at the very least, attenden a university lecture on a STEM field, should not, (and hopefully will not) be allowed to ever post his proletariat nonsense on /sci/".

The fact thay you dont understand the concepts of calculus does not imply that calculus is wrong, it implies the rather obvious,and that is that youre a retard.

Please kill yourself, at the very least castrate yourself.

>>9718677
this is the most retarded thing i've read all day

>>9717619

>Let's take 5 divided by zero. That's obviously equal to 0, since 5 * 0 equals zero.

What OP is saying is dumb dumb.

You are getting at 0*0 = 5

Dissagree

>>9717619
2/0 = 0 = 5/0
2 = 0*0 =5
Makes for some useless math.

>>9722326
wouldnt u feel guilty if he actually castrated himself. YEAH YOU FUCKING WOULD. jerk.

>>9718931
>>9718866
There's a multi-trillion dollar gaming industry that'd like a word with you.

>>9721706
Prove it.

>>9722535
>>>/g/hetto

>>9722546
5/-0.1=-50
5/-0.01=-500
5/-0.001=-5000

need some more?
tough shit, I'm out of crayons and sock puppets

>>9722563
Oh no I forgot a pixel, my bad [eqn]\lim_{x\rightarrow 0^+}\frac{5}{x} = \infty[/eqn] pretty dumb thing to get hung up on considering I wrote that a limit equals infinity instead of saying it doesn't converge.

>>9721694
wtf r u talking about
a number being between -inf to +inf is just any real number, its a valid statement, I didn't say it was infinity
0/0 is undefined but is an indeterminate answer when working with limits, and needs to be reworked to find the true answer

>>9722326
The fact a variable 'x' is throwing you for a loop means you dont even understand algebra let alone calculus. Go be a dumb nigger somewhere else.

>>9722733
Your sum statement makes no sense you fucking retard. You define a sum of n terms of a sequence thats in terms of x.
Your sum only converges y x = 0. Not for any integer x.
What the fuck are you even trying to say?
Have you even gone past calc 2 or are you just some youtube watching conspiracy nigger.
For fucks sake don't attempt to discuss subjects you lack the brain power to understand.
People like you are ruining this site.

>>9722757
Substitute x for 1.

Accept you dont have a highschool education and go talk about ponies or pokemon on /b/ or something.

>>9722757
Oh you know what i am the dummy.

You ought to have known i meant [math]\sum_{n=1}^{\infty} \frac{x}{(x+1)^{n}}[/math]

>>9721927
The counter to your response of mocking "real time" was literally in the same post you quoted, which denied plausibility to arbitrary time where n=infinity might be achievable.

Put it this way, if you treat sum[math]\frac{1}{2^n}[/math] up to [math]\frac{1}{\infty}[/math] as a numerical value, or more aptly sum[math]\frac{9}{10^n}[/math] since this one produces only 9's, for every real number n under infinity you get more 9's until infinity which produces terminating zeros, as [math]\frac{n}{\infty}[/math] ought to equal 0. This is just one of many many examples of infinite summation being retarded because infinity is retarded and treated as a number in higher math, when it really really really really isn't even relateable to numbers at all; being unable to perform any similar function that real numbers and even imaginary numbers can. Even this example would show that in arbitrary unreal time where infinity could be achieved, doing so invents termination, thus [math]0.\overline{9}[/math] truly is not the same number as 1. This is further shown through the implication that the infinite property of the sum truly should mean "unending", which also means there exists no decimal cutoff of accuracy and implies a requirement of infinite arbitrary decimal places that need to be filled.

For 7 decimal places, would you say [0.9999999] is equal to 1?

For 2 decimal places like with dollars, would you say 0.99 is equal to 1?

No. Of course not. You accept that there is always some small remainder, but you get retarded about infinity and deny a small remainder can exist there too.

0.99] 99 cents is not 1 dollar
0.999] 999 grams is not 1 kilogram
0.999...] [math]0.\overline{9} \neq 1[/math]

>>9722888
>let's pretend infinity is finite

>>9722827
>>9722827
Well that series converges if [math] \frac{1}{|x + 1|} < 1[/math] not for any integer, what makes you think I would say that converges for any integer?

>>9717681

>>9723263
He's right you fucktard. If you say, "x divided by zero should be zero" then you're saying:
x / 0 = 0
-> x = 0 for any x in R

>>9723009
You're tasked to count every real number between 0 and 1, starting from 0 and counting up.

You never reach 1.

Never as in never ever.

>>9723009
Reaching infinity is finite, yes. If you could reach infinity, there exists no greater value to increase towards. It's a finite end. Infinity is not supposed to be reached, but higher math simply ends up treating it as an arbitrarily large number which can be reached.

If you accept n=infinity never occurs in an infinite sum, you accept that you're not really doing infinite summation. You also accept there exists a finite decimal place of accuracy sought, and truthfully only do summation towards meeting that finite'th decimal place.

0.9 is not 1
0.99 is not 1
0.999 is not 1
0.9999 is not 1
0.99999 is not 1
0.999999 is not 1
0.9999999 is not 1
0.99999999 is not 1
0.999999999 is not 1
This shit never ends. Its never 1. And even if it were in a single case, there would exist infinite cases before it that said the value wasn't 1, which puts more strain on your brain when you thought you were comfortable with ignoring anything which might occur [math]after[/math] infinity.

>>9722733
your sum didn't make sense though
you set a sum of n, but have no n in the term. You also have to define x as a variable

>>9723348
>0.3 is not 1/3
>0.33 is not 1/3
>0.333 is not 1/3
>0.3333 is not 1/3
>0.33333 is not 1/3
>This shit never ends. Its never 1/3. And even if it were in a single case, there would exist infinite cases before it that said the value wasn't 1/3.

>>9723380
correct

>>9723419
Nice

>>9717619
you can't divide by zero because 0 isn't a number. trying to divide by 0 is like trying to figure out where nowhere is or how long you have to wait until never

>>9723348
>>9723348
Do you know what convergence is brainlet?

>>9717622
>destroy the apple

>>9723419
[math]\frac{1}{3}_{12}=0.25_{12}[/math]

>>9723659
some series converge to infinity

>>9723659
The only people who pretend to know how convergence works are the same retards who believe divergence isn't literally the same thing. If a sum continues to grow towards infinity, it is considered divergent. If you map all real numbers between 0 and infinity to between 0 and 1, this doesn't mean you're converging to 1. It is still just diverging to infinity.

>>9723419
How does that work

>>9717619
>It doesn't make sense.

Ask Siri for a clever answer to this question.

Let x = 5/0. Therefore x * 0 == 5. No number times 0 equals 5, therefore x is undefined.

This proof is valid for all real nonzero real numbers. I don't have a corresponding proof for x=0/0, since x * 0 == 0 is true for all real values of x.

>>9723348
>Reaching infinity is finite,

>>9723419
0.3=3/10+1/30
=0.33+1/300
=0.333+1/3000
=0.3333+1/30000
This shit never ends. It's always 1/3

1/3= 0.333...+1/inf = 0.333... + 0 = 0.333...

>>9723419

1/3=3/10+1/30
=0.3+1/30
=0.33+1/300
=0.333+1/3000
=0.3333+1/30000
This shit never ends. It's always 1/3

1/3 = 0.333... + 1/inf = 0.333... + 0 = 0.333...

>>9723822
looks like you have a problem with the decimal representations of fractions. If there are infinitely many 3s after the decimal then the difference between the fraction and decimal would be 0

>>9723843
>problem
feel free to type the faulty line

>>9723822
>>9723766
1/3 > 0.3
1/3 > 0.33
1/3 > 0.333

[math]\frac{1}{3} > 0.3\rightarrow[/math]

It works because thats how division works.

>>9723860
>>9723009

it's just a meme op you can definitely divide by zero if you put your mind to it

>>9723009
Infinity is unrelated to numbers. It has no meaningful number attributes like positive, negative, real, imaginary, complex, or even finiteness. This is the truthful definition of infinity.

Putting infinity on a number line is a brainlet mistake for the ages. Saying there exists no greatest number but infinity is also brainlet bullshit, cause that explicitly means it is finite because you can't go past it. Together, infinity on the numberline as a number that comes at the end because nothing can surpass it means it is finite.

Higher math was a mistake.

>>9723719
Converging to 1 is like saying you're converging to Titan.

Like, nigger, you're never going to Titan. You will never make it to Titan. You are no closer to getting to titan than Jupiter is. It doesn't matter what you or Jupiter does, neither of you will ever reach Titan. Jupiter is a lot closer to Saturn and Titan byproxy than Earth is, but Jupiter doesn't cross its orbit with Titan and neither do you, so for the sake of things it will take an infinite amount of distance traveled over an infinite amount of time, and this amount is equal for both you and Jupiter: infinite.

There is no such thing as "being close" to infinity. Infinity is infinitly far from anything. Infinity has an infinite difference from every number. An arbitrarily large number is no closer to infinity than 0 is. This "closeness" test is complete bullshit, so there is absolutely no sense in assuming [math]0.\bar{9}[/math] is "close" or "infinitely close" to 1. It isn't. It's infinitely far from 1, just the same as it's infinitely far from 0.9

>>9723924
>the truthful definition of infinity
stop talking out of your ass

https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity that is greater than every real number.

>>9718064
That's not correct. Take the limit as x approaches 0 for 1/x and you get -infinity or +infinity depending on which side you approach from. Mathematicians don't just say "fuck it," any function with a discontinuous limit like that is defined as undefined at the point of discontinuity.

>>9723933
it converges to 1 because it will never reach a value beyond 1 while simultaneously being able to cover all the values below 1
you converge to titan because, in a straight line, you will never go beyond titan while simultaneously covering all the distance between titan and wherever you came from
retards like you seem to forget about this part

>>9723977
Retards like you give credence to convergence when divergence is used in the contrary while meaning the same exact thing as convergence. Fucking nut.

Learn to read posts bro. The concept of convergence in calculus is invalid hand wavy poorly prescribed garbage for literal fucking retards.

>>9724084
You dont understand the very concept of infinity.
It can be positive, negative or complex.
But its an unbounded quantity. (Not exactly a quantity).
You have to understand all numbers represent ideas, infinity represents a different idea from all other numbers, hence why its not considered an "actual" number.
Heres a thought experiment for you:
Think of any any number.
Now think of any other number thats smaller or larger than your first number.
Count how many times you can do this.

>>9719605
But this would work for any number that's not 5. So 0/0 is all real numbers

Is this the new 0.999... bait?

>first time on /sci/
>see this thread

maybe this board isnt for me

>>9724749
dumb frogposter

>>9723977
Not only does it never reach a value beyond 1, it never comes close to reaching 1 in the first place. Convergence and divergence are useless and retarded.

5/0=5

>>9725087
Welp, forgot about signal processing and Taylor series approximations boys, this fag just said it's impossible to do so don't bother.

>>9725142
[math]"\approx" \neq "=" \\ \frac{1}{3} \approx 0.\bar{3} \\ 0.\bar{9} \approx 1 \\ \frac{1}{3} \neq 0.\bar{3} \\ 0.\bar{9} \neq 1 [/math]

Approximation is not equivalence.

>>9725172
It's literally just truncation of the infinite series in these examples, but okay you constructivist loon.

>>9725173
>truncating is infinite

>>9725178
>implying
Truncating is finite, a step your feeble mind demands to avoid considering logically consistent results like convergent infinite series.

>>9725182
>"infinite sum just means finite to an arbitrary point which i wont proclaim where that is until I personally decide to make up how much information i want, so because i'm not saying which obviously finite point i'm going to end on, you can't tell me that i'm not doing it infinitely :^)"

>>9725190
>I have a whole folder of brainlet wojacks to post, which I supplement with intentional misrepresentations of my opponent's argument
just fucking kys

An infinite series is technically defined as the limit of the sequence of partial sums.

Answer is A but does anyone have the explanation to this?

>>9718895

>>9725204
Limit is meaningless for fraction work like [math]\frac{x}{(x+1)^n}[/math].

Take [math]\sum_{n=1}^{\infty} \frac{18}{10^n}[/math] for example. That just "converges" to 2. Its just 9/10^n × 2. You dont need calculus to determine this. Converging to any number is retarded and easy, even though converging to a number under "infinite" summation is just mapping a divergence towards infinity to towards a number, but the base mechanics dont change. It never teaches infinity in divergence and it never reaches the limit in convergence. This would be less retarded if convergence wasn't seen as positive assertive equivalence while divergence seen as negating or null info.

>>9725172
.9999...=a
10a=9.9999....
10a=9a+a
9.9999...=9a+0.99999...
9=9a
a=1=0.99999...

[math]
x= \frac{1}{10} \\
0. \overline{9}=9x+9x^2+9x^3+9x^4+ \cdots \\
0. \overline{9}=9x \left (1+x+x^2+x^3+ \cdots \right ) \\
0. \overline{9}=(1-x) \left (1+\mathbf{x}+x^2+\mathbf{x^3}+x^4+ \cdots \right ) \\
0. \overline{9}=1-x+ \mathbf{x-x^2}+x^2-x^3+ \mathbf{x^3-x^4}+x^4-x^5+ \cdots \\
0. \overline{9}=1
[/math]

>>9718203
>We can divide by zero if we don't actually DIVIDE anything
Well it's not like that's wrong

>>9726158
0.999 = a
10a = 9.99
10a = 9a+a
9.99 = 9a + 0.999
9a = 8.991

Looks like you invented an extra 9 at some point.

Infinity doesn't mean "i can change how many numbers there are".

>>9726264
>inf = 3

k

>>9726264
[eqn].\bar{9} = 9*.\bar{1} = 9\sum_{n=1}^{\infty} \frac{1}{10^n} = 9\frac{\frac{1}{10}}{1-\frac{1}{10}} = 1[/eqn]
If this doesn't convince you then you're hopeless.

>>9726280
>>9726291
Stop inventing extra 9's

This is equivalent to what you're saying:
>x = 0.999
>10x = 9.999
>you're fucking up right here because 10x is actually 9.99, not 9.999 . You're forgetting to shift the decimal over and instead just invent an extra 9 out of thin air that wasn't accounted for in the first place to literally redefine a variable mid-equation.
>10x - x = 9.999 - 0.999 = 9
>9x = 9
>x = 1

Learn to do math you babbling gooks. If you're going to be retarded and treat infinity like a number, then fucking treat it like a number and not some arbitrary lala-land fantasy bullshit variable that can pretend to be any value you want to the effect of making you look insane and mentally challenged.

If there are an infinite amount of 9's, then there can be no greater amount of 9's. The correct procedure is:
[math]x = 0.\bar{9}\stackrel{\infty}{\rightarrow} \\ 10x = 9.\bar{9}\stackrel{(\infty -1)}{\rightarrow}[/math]
And before you go into some more lame and gay hand wavy garbage or misdirection about
>infinity - 1
just take a goddamn single second to realize a value less than infinity is still in the real numbers instead of your retarded method of trying to introduce an extra 9 to a value that already has the maximum amount of possible 9's, aka going beyond infinity.

>>9726350
[math].\bar{9}[/math] is shorthand for the convergent geometric series [math]\sum_{n=1}^{\infty}9\frac{1}{10^n}[/math] which is exactly equal to 1.
This fact is elementary and any student of mathematics should be able to prove it. The expression is perfectly well defined, and involves no such use of "infinity as a number" or whatever other nonsense your post is failing to convey.

>>9726350
Quit shilling lame dick notation

>>9726352
[math]0.\bar{9}[/math] is shorthand for repetitive 9's you goofy nigger. Stop making up retarded bullshit and kys.
What faggot country did you grow up in where you weren't taught fucking basic division.

>>9726353
Quit doing retard math so i don't have to use notation that jumpstarts your neurons.

>>9726352
>[math]0.\bar{1} × 9 = 1[/math]
>[math]0.\bar{1} × 9 \neq 0.\bar{9}[/math]
>implying

>>9726352
[math]\frac{1}{9} > 0.\bar{1} \\ \frac{2}{9} > 0.\bar{2} \\ \frac{1}{3} > 0.\bar{3} \\ \frac{4}{9} > 0.\bar{4} \\ \frac{5}{9} > 0.\bar{5} \\ \frac{2}{3} > 0.\bar{6} \\ \frac{7}{9} > 0.\bar{7} \\ \frac{8}{9} > 0.\bar{8} \\ 1 > 0.\bar{9} [/math]

>>9726362
>>9726366
>>9726377
The decimal representation "r" of a given number is defined as follows [eqn]r = \sum_{i=0}^{\infty}\frac{a_i}{10^i}[/eqn]
letting [math]a_0 = 1[/math] and [math]a_i = 9[/math] [math]\forall \space i\in \mathbb{N} [/math] We arrive at the definition of the symbol [math].\bar{9}[/math].
[eqn].\bar{9} = \sum_{i=1}^{\infty}\frac{9}{10^i} = \frac{\frac{9}{10}}{1-\frac{1}{10}} = 1[/eqn] by the convergence theorem for geometric series due to Euler. Any questions?

>>9726377
Each of those inequalities is false in the real number system. See my proof above.

>>9726379
>m-muh convergence
>i-if i rewrite the equation it'll surely work!
>>9724084

Only question i've got is what faggot country are you from where they don't teach you how to do math.

>>9726384
Is there an issue with my proof? I could prove that it converges but Euler did it for me a few centuries ago.

>>9726382
[math]\frac{1}{3} > 0.3 \\ \frac{1}{3} > 0.33 \\ \frac{1}{3} > 0.333 \\ \frac{1}{3} > 0.3333 \\ \frac{1}{3} > 0.33333 \\ \frac{1}{3} > 0.333333 \\ ... \\ \frac{1}{3} > 0.\bar{3}[/math]
its as simple as it can be, dude. Theres no excuse to fuck this up. Maybe you're still just fucking up only on the definitions of approximation and equality, but that has been covered already too.
>>9725172

>>9726390
Each of those inequalities is true, except the final one, which fails by definition.
[eqn].\bar{3} \equiv \sum_{n=1}^{\infty}\frac{3}{10^n}= 3\sum_{n=1}^{\infty}\left({\frac{1}{10}}\right)^n = 3\frac{\frac{1}{10}}{1-\frac{1}{10}}=\frac{1}{3}[/eqn]

>>9726363
>retard math
look who's talking with his retard kindergarten doodles

>>9726390
Do note that [math].\bar{3}[/math] does not represent that sequence you posted, but is defined to be the limit of that sequence. Which is exactly [math]\frac{1}{3}[/math]. Perhaps that's where you're having trouble? That sequence does never reach [math]\frac{1}{3}[/math] but it's limit is [math]\frac{1}{3}[/math]. Good on you for questioning what's presented and thinking about infinity, but the symbol is defined to be the limit.

>>9726390
Let me explain it another way. [math].\bar{9}[/math] is defined to be that very same number a finite string of 9s never reaches, which is the number 1. Therefore when we write [math].\bar{9}[/math] we mean the number 1. So you can maintain your intuition that it never quite reaches 1 while still accepting that its limit is 1, and we're speaking in terms of limits when we invoke infinity, whether it's with bars or dots

>>9726390
[math]\frac{7}{8} > 0.8 \\ \frac{7}{8} > 0.87 \\ \frac{7}{8} = 0.875 \\ \frac{7}{8}
= 0.8750 \\ \frac{7}{8} = 0.87500 \\ \frac{7}{8} = 0.875000 \\ \frac{7}{8} = 0.8750000 \\ ... \\ \frac{7}{8} = 0.875\bar{0}[/math]

its a lot different with a non repeating final answer. The closest chance you can come to saying 1/3 actually equals 0.333... is if [math]\sum_{n=1}^{\infty} \frac{3}{10^n}[/math] produces terminating zeroes at n=infinity on [math]\frac{3}{10^\infty} = 0 [/math], but even that works against your logic since that then means [math]0.\bar{9}[/math] must then be its own seperate number from 1 since it has terminating zeroes after it.

Fucking infinity-abusing donkeyshit brainlet. I'm tired of this garbage conversation. You've been given the info you must learn anf if you don't learn it then it is your own fault.

>>9726412
>[math]0.\bar{1} = 0.\bar{1}[/math]
>[math]0.\bar{2} = 0.\bar{2}[/math]
>[math]0.\bar{3} = 0.\bar{3}[/math]
>[math]0.\bar{4} = 0.\bar{4}[/math]
>[math]0.\bar{5} = 0.\bar{5}[/math]
>[math]0.\bar{6} = 0.\bar{6}[/math]
>[math]0.\bar{7} = 0.\bar{7}[/math]
>[math]0.\bar{8} = 0.\bar{8}[/math]
>[math]0.\bar{9} = 1[/math]
One of these things is not like the others. Quit posting, every time you do you just say more stupid shit.

>>9726420
Each of those equalities is provably correct. Conveniently, I have already proven the last one for you.

>>9726421
I warned you and you did it anyway. You posted again and just as predicted, you said more stupid shit.

>>9726423
Do you understand what the word "proof" means, frogposter?

>>9726414
With infinite sums, 'to approach' and 'to equal' are the same thing.

>>9726424
Yes. You dont. You provided an infinite sum equation, not a proof, and further did so when one of the biggest points of the conversation being about how convergence, infinite sums, and the concept of infinity as a number, are all fantasy brainlet garbage.

You don't know what a proof is. Your "proof" is worth as much as
>source: me
So fuck off, brainlet.

>>9726420
1/9 = 0.111...
2/9 = 0.222...
:
:
8/9 = 0.888...
9/9 = 0.999... = 1

>>9726425
Unironically, "APPROach" and "APPROximate" have a lot more in common than what you're claiming.

Knock knock is anyone home

>>9726428
Nope, I proved the equality using the definitions. It's not my fault you don't understand infinity nor convergence. It must be tough having such a low IQ. My source is Euler, not myself. He is the one who proved the formula for a geometric series. I can't imagine being so mentally handicapped that you cannot wrap your mind around concepts understood in the 1700s.

>>9726434
an idiot wrote both of them in a shitpost
fuck off back to >>>/lit/

>>9726433
>9 DIVIDED BY 9 IS EQUAL TO INFINITE 9'S CAUSE I LEARNED MATH AS WELL AS ALL LIFE LESSONS FROM A DEAD SQUIRREL I FOUND IN MY BACKYARD

>>9726443
>i have no argument

>>9726443
Nope, read "Elements of Algebra" by Leonhard Euler. If you can read, that is.

>>9726436
>dead ancient people can't be wrong.
gr8 defense m8

>>9726443
newsflash: 9*(1/9)=9/9

>>9726447
It's a proof. It's proven. It's not wrong. What part of this is hard to understand? Are you so mathematically inept that you cannot even verify a proof for yourself?

>>9717619
But so does 6*0 and 7*0 and everything*0. So the result of x/0 is simultaneously every number, so is undefined.

>>9726448
Newsflash
[math]\frac{1}{9} > 0.\bar{1}[/math]

>>9726453
[citation needed]

>>9726453
Wrong.
[eqn].\bar{1} \equiv \sum_{n=1}^{\infty}\left(\frac{1}{10}\right)^n = \frac{1}{9}[/eqn]

>>9726449
This isn't law. Its not like euler can't be tried twice for the same crime.

Fuck off dude. You're an idiot. You dont know how to consolidate math as a language and instead pretend to think you're intelligent by arbitrarly changing the fundamentals of arithmetic on a per-equation basis. This isn't even math, it's just gay and lame, so go be gay and lame somewhere else.

>>9726453
This is honestly one of the saddest displays of ignorance I've ever seen. I can't imagine being so proud of one's own stupidity.

>>9726458
It is math, in particular it's Real Analysis, a deep and complex subset of mathematics. The theorems and definitions I have cited are all well-defined and provably correct.

>>9726454
[math]\frac{1}{9} > 0.1\rightarrow[/math]
Keep adding 1's after the arrow.

>>9726464
Your expression is not well-defined, and if it were the only sane definition would be [math]0.1 \rightarrow \space= \space \frac{1}{9}[/math]

>>9726464
>fuck off back to >>>/lit/
kek, you and your doodles

>>9726458
I know your type. You failed calculus and now you have a grudge against it. Sad

>>9726470
Its well defined by basic division which predates calculus by thousands of years a dumb cunt.
Do the fucking math
1÷9 = what
First term
0.1
Still a remainder
Second term
0.11
Still a remainder
Third term
0.111
STILL a remainder

Move to hawaii and die in a lava flow you creepy slop of brain diarrhea.

>>9726479
So basically you're defining a sequence that can be made arbitrarily close to [math]\frac{1}{9}[/math] sounds like a limit to me.

>>9726479
>let's pretend infinite is finite
stop pissing in your cereals

>>9726479
Do you realize you're literally using division to construct [math]\sum_{n=1}^{\infty}\left(\frac{1}{10}\right)^n[/math], which is equal to [math]\frac{1}{9}[/math]?

>>9726479
You're dividing and adding the remainder. You're adding an infinite number of remainders. An infinite sum. Congratulations for finding an alternative derivation of the exact same number.

>>9726485
>>9726486
>>9726488
You're godless idiots.

>>9725172

>>9726493
The symbol [math].\bar{9}[/math] is defined to be the limit which is provably 1.

>>9726492
How did you miss this. All i did was prove pic related, my point, and suddenly you agree with me after disagreeing cause you have literal goldfish intelligence.

>>9726495
Which symbol

>>9726498
[math].\bar{9}[/math]
>>9726497
I saw that and gave multiple proofs to its inaccuracy. Please only discuss concepts you understand in the future, for your sake and ours.

>>9726501
Which symbol
[math] . \qquad 9 \qquad \bar{ }[/math]
which one.

>>9726504
The composition of the three. Sorry if that wasn't clear enough for you.

>>9726486
Where do you assume to have stopped getting a remainder instead of infinitely getting a remainder? Its almost like you greentexted the reply you yourself deserved instead of actually quoting or responding.

>>9726506
Three symbols is not a symbol.

[math]0.\bar{9}[/math] is not a symbol.
It is a number. Its a number you can craft with the decimal system. Considering you're a godforsaken brainlet and probably use calculators for much everything, [math]0.\bar{9}[/math] is roughly equal to 0.999999999999999, or just 0.9999999 when you feel like the Casio will do you well.

In any case, far from infinite, and far beyond your grasp of how calculation is actually performed. There is nothing left to say to you other than "You're delusional" if you honestly believe a repeating decimal is somehow a symbol with deeper meaning related to euler and calculus. So.
You'rw delusional.

Seek help [math]\text{senpai}[/math]

>>9726519
Wrong.

>>9717619
Brainlet here making a 5th attempt at reading Penrose's "Road To Reality".
In the first few chapters, he provides a chronology of number system expansions. Natural numbers to integers/rationals to the system of reals and finally complex numbers. Keep in mind, giving a "value" to sqrt(-1) was once considered meaningless or at least treated with skepticism. Maybe we need to expand our notion of a "number" yet again to unify physics (ToE)?
Is the formal symbol for divide-by-zero considered "infinity" or is it considered meaningless? If not, does it make any sense to adjoin x/0 to the number system in a more formal way, a more useful way? If not this either, is there some other meaningful way we can extend our number system? Does it make sense to give a duality to zero whereby any divide-by-zero can be treated as divide-by-infinity instead? Go easy on me, I'm just spit-balling.

>>9726522
You've lost so much you can barely muster a single word.

>>9726524
Incorrect. A construction is given on page 11 of "Principles of Mathematical Analysis" by Walter Rudin

>>9726523
Neither 0 or infinity are Real Numbers so there is no sensible arithmetic to be performed with them.

May as well try to calculate 1 ÷ salmon

>>9726507
word salad, take your pills and try again

>>9726529
>no sensible arithmetic
5+0=5
>mind blown

>>9717619
.9999999=1
whoo says you can't divide 5 by zero

>itt
>undergrads and people who failed calc

>>9726264
lmao seriously?

1-0.9999...=???

2/7=0.285714285714...
+
5/7=0.714285714285...
=
7/7=0.9999....

>>9726628
1/inf = 0

>>9726636
1/9 = 0.111...
+
8/9 = 0.888...
=
9/9 = 0.999...

>>9726529
>>9726523 here.
That's sort of what I'm getting at. Once upon a time sqrt(-1) was nonsensical. I'm not saying there is a formal way to join a zer0-infinity duality to our number system. But your skepticism is an echo of past treatment of irrationals and complex numbers. I fully admit I'm a brainlet, but I often wonder what we are missing wrt unifying physics. Number system expansions, whether forced upon the ancients (irrationals) or just a curiosity at first (complex plane) has had direct relevance to physical reality. What number system expansion is needed now to unify GR and QM?

>>9717619
5 divided by 0 is still 5. Prove me wrong.

>>9726753
>Pedro gives away 5 apples equally to 0 persons.
>Therefore Pedro has 5 apples left
Check m8 atheists

0/infinity=infinity/0

>>9717619
absolute state of this website

>>9727263
This is depressing. /Sci/ used to be an enlightened board.

In a fraction u can define zero if u use limit , like lim1/x as x goes to zero , but x never takes actually 0 . (5/0)=y => 0*y=5 which doesnt exist

>>9726547
>performing arithmetic when there is literally no reason to do so as no change will occur is sensible
>wasting time and energy is sensible

>>9728359
https://en.wikipedia.org/wiki/Moving_the_goalposts#Logical_fallacy

>>9726710
Infinity doesn't need to exist and thats the problem right there. It is essentially just alternate of eternity, but treated as a number in math has created tremendously stupid fields and equations. So yea, there are some ways math could change sure, but they involve getting away from infinity outright. Also since the internet has come about, rate of prestablished information being positively change has decreased. We're sooner to lose all higher maths than infinity as liberal for profit universities go full communism to indoctrinate their students with intentionally bad math supportive of fringe foreign government policies, which will eventually become no math at all with the increased reliance on "smart" devices and generations of learning about how much money you're entitled from the government.

outlook is grim.

also zero + infinity just look like a dick and balls.

[math]\rlap{\; \text{0}}{\infty}[/math]

you have 1 and divide it once don't you hab 0.5 each kekekeke

>>9718607
Wish we could cull all stirner brainlets