/sci/ - Science & Math

>>9742117

Could you be more specific? What do you mean by "exponential function approaching 0"? Write it as a number you want us to evaluate, please.

Can someone refute this
1/3 * 3 = 3/3 = 1
1/3 = .333...
.333... * 3 = .999...
1 = .999...

>>9742144
I think my preclac teacher made a demostratio usign series also?

>>9742117

0.9999.. does not = 1

you do not understand limits

>>9742362
no u

>>9742121
y= e^x

>>9742144
so clunky
1/3 = 0.3...
+
1/3 = 0.3...
+
1/3 = 0.3...
=
3/3 = 0.9...

>>9742362
You can't even type an ellipsis correctly

>>9742362
Wikipedia says it does.

>>9742362
It does you brainlet. .999... is an additive inverse of 1.

1 + (-0.999...) = 0

>>9742362
Please don't tell me you're the faggot who thinks we should truncate all decimals instead of rounding them.

>>9742117
>pronouncing it laytecks

>>9742396
He's not who you're looking for. I am.

I thought i booty blasted you pretty well when we discussed this earlier

2/3 = 0.6666667 when you round

Thats not correct math.
Sorry, rounding is not intelligible. Also why convergence isnt intelligible.

>>9742401
Welcome back. How can we help you?
A new diaper perhaps?

>>9742362
choke on some epsilon-deltas you nigger

>>9742401
It's certainly closer to correct math than truncating it.
I proved you wrong in both your attempted examples by rounding up or down based on the next decimal place instead of just flooring everything, so I don't know where you're getting the idea you won.

>>9742117
0.999... is the result of a limiting operation
[eqn]\mathrm{lim}_{N\to\infty}9\sum_{n=1}^N\frac{1}{10^n}[/eqn]
which is just a geometric series and is precisely equal to 1, while [math]e^x[/math] is never equal to zero for any real number [math]x[/math], no matter how large in the negative direction.

However, if we take the limit as x tends to negative infinity we do get
[eqn]\mathrm{lim}_{x\to-\infty} e^x=0[/eqn]

Also note that if I cut off the sum at any finite N, I end up with a number not quite equal to one, no matter how large I take N to be.

[math]e^?\,=\,0.999...[/math]

>>9742482
[eqn]?=1-0.999...[/eqn]

>>9742144
.666... is an infinite number to actually use it it has to be rounded up unless you have infinite computing power. so
.666... is .667
.667+.333=1

your image is very interesting

but your question is dumb

>le reddit spacing

>>9742117
But they both use the same axiom for proof so i doubt you personally can explain why 0.999=1

>>9742614
>.666... is an infinite number to actually use it it has to be rounded up unless you have infinite computing power. so
Or just write it in base 3 and it's .2. Doesn't seem so infinite anymore does it?

>>9742117
[eqn]0.999\neq0[/eqn]

>>9742614
>infinite computing power
ever heard of floating point arithmetic you brainlet

these are my favorite threads

>>9742462
>"rounding is closer than truncating"
>says the guy getting a seven in his equation which cannot print anything but 6's

>>9743314
0.667 is closer to 0.666... than 0.666 is.
Go ahead. Try to prove it wrong.

>>9742370
What do you mean? Lim as x goes to 0 = 1. Lim as x goes to negative infinity = 0

>>9743554
top quality post m8 real good you sure showed him

>>9744186
Thanks, maybe he will finish elementary school and learn something about math.

>>9742117
>Can /sci/ explain why 0.999 = 1
Definition.

>but an exponential function approaching 0 never equals 0?
The limit does.

>>9742117

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

Therefore 0.999 = 1

By exponential function approaching zero I assume you mean a reciprocal, 1/x, which approaches 0 at increasing values of x.
Writing out the values given from the reciprocal function starting at x = 1 looks like the following.

1/1 = 1
1/2 = 0.5
1/3 = 0.333. . .
1/4 = 0.25

1/(10^6) = 0.000001

1/(10^G64) = 0.000. . .001

As you can see, as X grows towards infinity, Y diminishes towards zero. However, the value of Y = 0 is unattainable for any value of X on the number line, because every finite number will result in a finite number of divisions of 1.
One cannot set X = ∞ to attain Y = 0 either. However, we will proceed stating that 1/∞ = 0, and explore what that implies.

1/∞ = 0
(1/∞) * 2 = 0 * 2
(1/∞) * 2 = (1 * 2)/(∞ * 2)
1 * 2 = 2
∞ * 2 = ∞
0 * 2 = 0
2/∞ = 0
1/∞ = 2/∞

Therefore 1 = 2

Clearly something is wrong. If 1/∞ = 0, then all numbers divided by infinity equal zero, and by extension all numbers equal each other.
Furthermore,

1/∞ = 0
(1/∞) * ∞ = 0 * ∞
1 = 0 * ∞

2/∞ = 0
(2/∞) = 0 * ∞
2 = 0 * ∞

Again, the use of infinite seems to imply all numbers are equal. This is not the case. In reality, 1/∞ != 0 , there is no solution to 1/∞ because infinity is not a number. The outcome of the equation is undefined, and offers no meaningful result at X = ∞
Therefore, at Y = 0, there is a 'hole' or asymptote on the plot. Likewise, and for similar reasons, there is an asymptote at X = 0 as well, where the result of 1/0 is also undefined.

Why did I do this.

>>9742400
Lattecks

>>9742117
0.999... is a never-ending string of 9s. 0.00000...0001 still has an end.

>>9742144
It's circular reasoning and doesn't prove anything. You'll have to first prove that 1/3 = .333...

>>9742117
I knew /sci/ was full of absolute brainlets.

0.33333... is an incomplete expression. It represents 1 as constantly being divided by 3.
Now multiply 0.3333 by 3 you get 0.9999, which is equal to 1.

>>9744624
>all numbers divided by infinity equal zero, and by extension all numbers equal each other.

>let's pretend infinite is finite

>>9745492
which digit isn't 3 ?

the 1000th?

qed

>>9742362
How many times does someone have to write the proof for you retards to understand that [math] .\bar{9}=1 [/math]?

>>9745553
Why do you fail to see the irony in your "lets pretend" posts?
You're pretending infinity exists.

>>9745505
0.999.... is an incomplete expression. It represents the incomplete expression 0.333.... multiplied 3 times.

if you know 1÷3 doesn't have a strict equality in decimals, then you know multiplying that loose inequality by 3 returns a value that doesn't have a strict equality to 3/3

>>9746410
>0.999.... is an incomplete expression.
It's a complete expression of 1.

>if you know 1÷3 doesn't have a strict equality in decimals
It does, 0.333...

>>9746433
The repeating threes means there is no final element or an expanding 0 element. 0.333.... is an approximation of 1/3, not an equality.

>>9746441
>The repeating threes means there is no final element
Yes, but that has nothing to do with it being complete. Complete means that it has every digit, not that there is a final digit. In other words, there is no difference between 0.333... and 1/3. Now please tell me what 1/3 - 0.333... is.

>or an expanding 0 element.
Gibberish.

>0.333.... is an approximation of 1/3, not an equality.
Wrong.

0.333... = sum from k=1 to inf of 3/10^k = 1/3

>>9742117
[eqn] 0.\bar{9} \equiv \sum_{n=1}^\infty \frac{9}{10^n}=\lim_{k \rightarrow \infty} \frac{9}{10}\frac{1-\frac{1}{10^k}}{1-\frac{1}{10}} = \frac{\frac{9}{10}}{1-\frac{1}{10}} = 1 [/eqn]
now delete this thread and yourself

>>9746441
So the natural numbers are incomplete? They have no final element, so which natural number is missing?

>>9746454
1/3 - 0.333... = [math]\frac{1}{3} - 0.\bar{3}[/math]

you are trying to do math across two different number systems where the problem has already been shown to you to exist because one value does not translate to the other.

[math]0.\bar{3} \neq \frac{1}{3} \\ 0.\bar{3} = \sum_{n=1}^{\infty} \frac{3}{10^n} \\ \\ \frac{1}{3} \neq \sum_{n=1}^{\infty} \frac{3}{10^n}[/math]

>>9746441
[eqn] 0.\bar{3} \equiv \sum_{n=1}^\infty \frac{3}{10^n} = \lim_{k \rightarrow \infty} \frac{3}{10}\frac{1-\frac{1}{10^k}}{1-\frac{1}{10}} = \frac{\frac{3}{10}}{1-\frac{1}{10}} = \frac{\frac{3}{10}}{\frac{9}{10}} = \frac{1}{3} [/eqn]
This proof is flawless.

>>9746486
Your gay fallen trees aren't interesting.

>>9746494
The triple bar indicates a definition. Every step in this derivation is provably correct and also rather trivial.

>>9746484
>you are trying to do math across two different number systems
No, I'm not. The construction of the reals means that they are complete which means that all infinite decimals represent a real value. The only question then is whether 0.333... is 1/3 or some other value. So what is their difference?

>0.333... ≠ 1/3
False. See proof at the end of >>9746454 which you failed to respond to.

>>9746484
Let [math] \varepsilon = \frac{1}{3} - 0.\bar{3} [/math]. By the Archimedean property of [math] \mathbb{R} [/math], [math] \varepsilon [/math] is necessarily equal to [math] 0 [/math] (Why?)

>>9746484
>0.333... is an approximation of 1/3
>0.333... and 1/3 cannot be compared
Troll or hypocrite?

>>9746454
[math]\frac{1}{3} \neq 0.\bar{3} \\ \frac{1}{3} = 0.\bar{3}_{\frac{1}{3}} \\ \\ \sum_{n=1}^{\infty} = 0.\bar{3} \\ 0.\bar{3}_{\frac{1}{3} - 0.\bar{3} = 0.0_{\frac{1}{3}} \\ \\ 0.0_{\frac{1}{3}} × 3 = 0.0_{\frac{3}{3}} = 0.0_{1} = 0.\bar{0}1[/math]

also you have the gay and mental problems if you believe smallest parts cannot exist. Without smallest parts, larger parts cannot exist. You make no intelligible effort to explain how a value of 0.1 can exist so heres a magic sum

0.1 = 1 × [math]\frac{1}{10}[/math]
0.1 = 10 × [math]\frac{1}{100}[/math]
0.1 = 100 × [math]\frac{1}{1000}[/math]
0.1 = 1000 × [math]\frac{1}{10000}[/math]
0.1 = 10000 × [math]\frac{1}{100000}[/math]
0.1 = 100000 × [math]\frac{1}{1000000}[/math]

0.1 = infinity × [math]\frac{1}{10 \infinity}[/math]

>>9746547
[math]\frac{1}{3} \neq 0.\bar{3} \\ \frac{1}{3} = 0.\bar{3}_{\frac{1}{3}} \\ \\ \sum_{n=1}^{\infty} = 0.\bar{3} \\ 0.\bar{3}_{\frac{1}{3}} - 0.\bar{3} = 0.0_{\frac{1}{3}} \\ \\ 0.0_{\frac{1}{3}} × 3 = 0.0_{\frac{3}{3}} = 0.0_{1} = 0.\bar{0}1[/math]

>>9746513
Its literal retardation to believe smallest parts cannot exist indeterminable from nothing.

>>9746547
>also you have the gay and mental problems
Why the homophobia?
>Without smallest parts, larger parts cannot exist.
Wrong.
>You make no intelligible effort to explain how a value of 0.1 can exist so heres a magic sum
What?
>>9746553
>Its literal retardation to believe smallest parts cannot exist indeterminable from nothing.
What? The reals are necessarily such that no infinitesimal or infinite elements exist.
Your "proof" there shows that your proposition that they aren't equal requires a decimal expansion to both be finite and infinite. Therefore you have shown that assuming they're not the same number is contradictory. You literally just proved yourself wrong, I don't know whether I should be impressed or not. Who knew it was possible to be this dumb.

>>9746547
>>9746547
>also you have the gay and mental problems if you believe smallest parts cannot exist.
The smallest number does exist, it's 0.

>You make no intelligible effort to explain how a value of 0.1 can exist so heres a magic sum
See the construction of the rationals.

>0.1 = infinity × 1/(10*infinity)
Wrong. Try again.

>0.333... ≠ 1/3
False. See proof at the end of >>9746454 which you again failed to respond to.

>0.\bar{3}_{\frac{1}{3}}
What does this notation refer to? Try not to make up your own notation, standard notation is sufficient for this discussion.

>>9746553
>0.0_{\frac{1}{3}} × 3 = 0.0_{\frac{3}{3}} = 0.0_{1} = 0.\bar{0}1
So this is all just 0 or gibberish, since there is no digit at the end of infinitely repeating digits.

>>9742144
negro the definition of convergence is all you need

>>9746566
Standard notation is not sufficient in describing the difference. Doesn't mean the difference doesn't exist.

>>9746565
So what are you saying? If there are no aspects of infinity in the reals then voila, even 0.999.... must then have a finite expansion along with every other repeating decimal.

Don't tell me you didn't realize that is what you wrote.

>>9746572
>infinitely repeating
>infinite anything

>>9746581
The theory of limits does not require there be a real number that is infinite or infinitesimal. You're conflating two entirely different things. Infinity is associated with reals via limits, but that doesn't make it a real number.

>>9746588
So what is the last digit of 0.333...?

>>9746671
3

>>9746673
Which digit is the last?

>>9746581
>Standard notation is not sufficient in describing the difference.
It is, it's 0.

>>9746675
The last

>>9746677
It isn't considering it's not 0.

>>9746684
Yeah which one is that? 1st? 2nd? 3rd?

>>9746697
It is, see the proof you keep ignoring.

>>9746715
Do you think infinity is a number or an amount?
Like do you think an "infinite'th" decimal place exists? Do you believe "an infinite" amount of 9's repeating in 0.999.... or do you believe it's "an infinity" of 9's?

Since infinity is not a number, there cannot exist an infinite amount. The concept of this infinite amount object that you believe is validated is actually null, void, and undefined. There is a similar object in an infinity, but it doesn't effect to enumerate. The grotesque mentally challenged brainlet gymnastics occurs when mathleticians place infinity on or near a numberline. Infinity is not a quantity that can be enumerated to or even towards. It is an entirely seperate identity from the set of all numbers. Putting infinity on the numberline is like putting a couch in a cage as a Zoo attraction. Couches aren't wild animals. Infinity isn't a number.

"Infinite" is fucking nonsense btw. I think the word you're looking for is "indefinite".

Why do people even reply to threads like this? You already know from the OP that it's someone who's going to intentionally act daft.

You are just going to waste your time.

>>9746797
Ever so relevant

>>9746791
infinity is a number in [math] ^*\mathbb{R} [/math]
please only post about things you understand in the future

>>9746791
>Do you think infinity is a number or an amount?
Yes, for example the cardinal number representing the amount of natural numbers is infinity.

>Like do you think an "infinite'th" decimal place exists?
No, all decimal places correspond to a natural number and are unending like the natural numbers. Saying there are infinite natural numbers does not mean there is a natural number called infinity. That is simply a naive intuition caused by incorrectly applying the expectation that any finite ordered set of size n has an nth member. You rely on naive intuition because you are too stupid or too pigheaded to learn the rules of what you're talking about, this is the source of your difficulties.

>Do you believe "an infinite" amount of 9's repeating in 0.999.... or do you believe it's "an infinity" of 9's?
What's the difference?

>Since infinity is not a number, there cannot exist an infinite amount.
Infinity is a number though. Do you ever get tired of having these fallacious arguments debunked?

>The concept of this infinite amount object that you believe is validated is actually null, void, and undefined.
The only thing null, void, and undefined is the argument against infinity you keep pretending to have but won't show.

>There is a similar object in an infinity, but it doesn't effect to enumerate.
What does this mean?

>The grotesque mentally challenged brainlet gymnastics occurs when mathleticians place infinity on or near a numberline. Infinity is not a quantity that can be enumerated to or even towards.
What relevance does enumeration even have on the real number line? You cannot enumerate to *anything* on the real number line, let alone the extend real number line. What is your point?

>I think the word you're looking for is "indefinite".
The only thing indefinite here is your argument.

>>9746791
>Couches aren't wild animals. Infinity isn't a number.

Wow, powerful stuff.

>>9746841
It shouldn't be. It's trivially simple.

>>9746942
The only thing trivially simple here is you.

>>9742475
/thread

>>9746835
>this long shitpost of autistically replying to each sentence
>doesn't know what enumeration means

>>9746835
"An infinity" is a contained idea.
"An infinite -" "amount, quantity, number of, iterations, etc." is an invalid concept. There is nothing intrinsically pertaining explicitly to math ir even numbers in the idea of "infinity", and mathlets assume otherwise by trying to extend the identity of infinity to "an infinite" number.

By the implication or extended logical assumption of there being an infinity of 9's in 0.999.... , this does not mean that the 9's are countable, roundable or reduceable, which means functions like [eqn]\sum_{n=1}^{\color{red}{\infty}} \frac{9}{10^n} [/eqn] do not produce the classically desired result, given:
1. The misuse of infinity by placing it's invocation in the structure of the expression that asks for an amount of iterations
2. The obvious enumeration which occurs from the solving of partial sums is at ends with the structure of an object indicative of infinity lacking this feature.

Where "object" here is used to describe sets, both in theory or analysis of work accomplished to achieve a result.

Which means [math]\sum_{n=1}^{\infty} \frac{3}{10^n}[/math] is not only invalid math, but if it were valid the result of [math]0.\bar{3}[/math] is not the same literal value as the result from [math]\frac{1}{3} \approx 0.\bar{3} \text{ aka } \frac{1}{3}
= 0.\bar{3}_{\frac{1}{3}} [/math]

a more true representation of the classic infinite sum can or should instead be written as
[eqn]\sum_{\n=1}^{\stackrel{\rightarrow}{\mathbb{Z}}} [/eqn] which invokes to iterate through the set of integers. This gets away from the misinterpretation of infinity and clarifies the extent of accurate calculation. In the classic infinite sum, any arbitrary section of real finite partial sums exists to defy the unenumerable nature of an infinity, which without invoking infinity allows to strictly adhere to a sensible, enumerable result, thus using Z instead of a hard invocation of any specific limit too allows for arbitrary accuracy just the same. Such a sum [math]\sum_{n=1}^{\stackrel{\rightarrow}{\mathbb{Z}}} \frac{9}{10^n} = 0.\bar{9}[/math] can exist without sleights against common sense in knowing the enumerative nature of the sum structure, even if infinity were a valid input, should only create the same number object as the Z-iterative structure where finite accuracy is all that can be acquired, for when treating infinity with numerical properties in an iterative sum as in classical mathletism, only real finite partials of any arbitrary amount may be accounted for.

>>9746942

Actually, it's simply trivial.

>>9747234
Please explain to me how you can enumerate to a real number, retardo.

>>9742117
Idk, can you explain to me why 2d anime girls wearing bunnysuits arent real yet

>>9742117
Because one invokes limits and the other doesn't.

>>9747251
>"An infinity" is a contained idea.
Why do you base your arguments on vague, made up terms like "contained idea?" Use English.

>"An infinite -" "amount, quantity, number of, iterations, etc." is an invalid concept.
Wrong, look at the cardinal numbers.

This does not elucidate a difference, it just confuses the argument even more.

>By the implication or extended logical assumption of there being an infinity of 9's in 0.999.... , this does not mean that the 9's are countable, roundable or reduceable
Wrong, as I already explained, the decimals are in correspondence to the naturals, thus by definition they are countable. And what does "not roundable or reducible" even mean in this context? Is 1 "roundable or reducible." Stop pretending that your arbitrary use of mathematical terms is actual math.

>>9746402
in math, it does
you are shit in math, that's all

>>9742117
GOD DAMN IT SCI WHEN WIL YU LEAR>!

LIMITS LIKE 0.999... ARE NOT NUMBERS THEY ARE LIMITS> YOU ARE JUST ONE INCLUSION MAP SHORT OF SAYING IT EQUALS 1.
[math]\color{red}{\iota(0.999\dots) = 1}[/math]
GET IT THROUGH YOUR THICK FUCKING SKULL

>>9747251
>dunning-kruger in full force
Please refrain from posting until you graduate high school. Thank you.

>>9747234
>equivocation fallacy

>>9748148
You must be a prophet because your reply accurately described only your own reply after you hit post.

>>9747594
1 is not an object with a prescribed relation to infinity you dumb cunt, regardless if you approach this with either shitlet mathlet education or an attempt at using your brain to create original ideas. The topic is "repeating" decimals.

Infinity is not a number object. Its a self contained idea. It doesnt branch out into other ideas, such as the implement of an "infinite number" to be quite literally arbitrarily, vaguely, and inconsistently used in math as more of a fucking retarded magical plot device to get an answer. All implements of the infinite number in classical math read like a bad meme of
>1. expression
>2. invoke infinity
>3. ???????
>4. PROFIT

Because the rules and implements of infinity will often change dynamically even so far towards changing mid-fucking-equation after initially starting with a different infinite definition whose assignment as a variable or operator in an expression is not updated once the arbitrary change occurs.

It's goofy fucking garbage.

>>9748073
Um... real numbers ARE limits, as in they can be identified as Cauchy sequences of rationals modded out by some equivalence relation.

because 0,99999 etc will eventually be close to one something, if you divide something you'll never end up with nothing.
I know shit little about math and im still right lata faggots.

>>9742362
1 - 0.9999999... = 0.00000000...
0.99999999... = 1

3 × 4 = 12
0.33333 × 4 = 1.33332

[1].3333[2]
12

0.333... × 4 =
1.333...2

9 × 9 = 81
0.999... × 9 = 8.999...1
+ 0.000...9 = 1

0.000...9 = [math]\frac{9}{10^{\infty}}[/math]

If there can exist a number "infinity" to describe the repeating nature of the decimals we are working with, then this same number of "infinity" can be used in arithmetic.

If however we cannot use the number of "infinity" in arithmetic, then we cannot use the number of "infinity" to describe the repeating nature of the decimals we are working with.

keep it consistent folks.

>>9748612
n/inf = 0

>>9748325
>1 is not an object with a prescribed relation to infinity you dumb cunt
The real number 1 is constructed the exact same way as 0.999..., there's nothing special about either except that one triggers your retardation.

>Infinity is not a number object.
Wrong, it's a cardinal number.

>It doesnt branch out into other ideas
Wrong, most of mathematics uses it.

>Because the rules and implements of infinity will often change dynamically even so far towards changing mid-fucking-equation after initially starting with a different infinite definition whose assignment as a variable or operator in an expression is not updated once the arbitrary change occurs.
Can you give me an example? (no you will ignore this just like every other time you are asked to back up your ridiculous claims)

>It's goofy fucking garbage.
Yes, that it a good description of your fallacy filled posts which claim there is a problem with infinity but time and time again only illustrate the sheer idiocy of your "common sense."

>>9748612
>>9748612
Ah yes, this is new proof method is revolutionary. Observe:

1 < 5
2 < 5
3 < 5
4 < 5

I think we can all see the pattern here. Therefore we can conclude that 72 < 5. Clearly this means standard mathematics is broken and mathematicians must get to to work on a new system that does away with ridiculous ideas like "72 > 5"

>>9748887
>n/inf = 0
then
n = 0*inf
inf=n/0

>>9748968
Are you a faggot?
Are you a homosexual?
I find that queers, once having fucked up the most basic of himan endeavors being heterosexuality, usually carry that inverse intelligence into every other facet of life, which would certainly fucking explain why you seem to be literally fucking retarded.

Fuck off faggot. One country under God.

>>9748950
>>9748612

>>9748950
Tell me which element of A is identical to B

A: [ 1 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...]
B: [ 0 . 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 ...]

is it the first element?
A1: [1] & B1: [0]
these aren't the same

is it the second element?
A2: [0] & B2: [9]
these aren't the same

Which element is the same between A and B?

tough, but possible!!!

Reminder that vague continuities are not a valid expression in real math.
[math]0.\bar{n}[/math] or 0.nnn... don't mean anything. You're just truncating some efforts by implying unending repetition, but then you will turn into a gay garbonzo when you believe you don't truncate your efforts elsewhere.

Just admit it. Theres no such thing as an infinite number. You're just doing finite finitist work.

>>9742475
Good post. I think the crux of the issue here is that while you can't evaluate e^x at negative infinity, you can both find and determine the sum of an infinite series, provided of course it's not divergent.

>>9742117
>e^-x*sin(x)

Eat shit.

>>9742614
>what is induction schema

>>9749128
Why the homophobia?
>>9749161
It's well defined:
[eqn] 0.\bar{9} \equiv \sum_{n=1}^\infty \frac{9}{10^n}=\lim_{k \rightarrow \infty} \frac{9}{10}\frac{1-\frac{1}{10^k}}{1-\frac{1}{10}} = \frac{\frac{9}{10}}{1-\frac{1}{10}} = 1 [/eqn]
If you can't even understand this simple derivation then you're beyond help.

>>9749128
You are one triggered retard.

>>9749134
>>9748968

>>9749152
Tell me which element of A is identical to B

A: [1+1]
B: [4÷2]

is it the first element?
A1: [1] & B1: [4]
these aren't the same

is it the second element?
A2: [+] & B2: [÷]
these aren't the same

Which element is the same between A and B?

tough, but possible!!!

>>9749152
https://en.wikipedia.org/wiki/Construction_of_the_real_numbers

>>9748977
>0*inf
inf isn't a number, retard

0*inf is like that shitpile "unstoppable force meets an immovable object" meme

it doesn't make any sense and is undefined

>>9749247
>inf isn't a number
neither is 0
it's a match made in heaven

>>9742144
The generality of algebra was refuted some centuries ago sweetie.

>>9749230
values aren't expressions.

>>9742117
if they were different numbers you would be able to find a number x such that 0.9999... < x < 1

>>9749421
Values are not decimal representations.

>>9742117
Because that function has no numerical value. You could call it negative/positive infinity

>>9749421
The entire point of constructing the real is to define them as expressions of rational numbers. You couldn't be farther from the truth. This is especially ironic considering you were attempting to respond to my claim that 1 is constructed in the same way as 0.999... (both employ infinite limits or infinite sets somewhere in the construction). Instead of showing me that you understood what those constructions were, you responded with more decimals. You are completely out of your league and you know it. Fuck off.

>>9742117
Can someone explain why x=1 is 1 but x>0 is not 0

>>9742372
Let me explain it in a way you can understand:
Suppose you try kiss your gf (we've all done this, right)
and 1=you kissing your gf
So how close do your lips need to be in order for it to be considered a kiss?
The closer you get to her the smaller the smaller the distance in between but there could always be a little bit further that you push your lips closer
So you are 0.9999 units of distance away from properly kissing your gf
And then 0.99999
And then 0.999999
And it goes on 0.99999...
But after a while that distance gets physically impossible to get smaller so you have kissed your gf (in a very creepy and violent way)
And so you get 0.99....=1

>>9749947
>suppose you kiss your girlfriend
Why the homophobia?

>>9749962
The answer is an exponential function approaching 0 never equaling 0
No h0m0

>>9749947

let's pretend infinite is finite

>>9749962
>phobia
being disgusted by something isn't a phobia. I don't like touching or looking at turds, but I don't panic every time I take a shit

>>9750251
A phobia can also be an aversion

>>9749853
They sure are.

>>9749887
You're the retard who doesn't believe [math]\frac{\bar{9}}{1\bar{0}}[/math] isn't valid, cocksucker. Eat shit and die, you goofy niggerbrained psuedofunctioning sack of donkeyshit.

>[math]0.\bar{9} \text{ exists but } \bar{9} \text{ doesn't.}[/math]

>>9750539
>>9750549
awwwww it's shitlatexman

______9._______
______9.9______
______9.99_____
>yes goy. Yesss...
______9.999____
______9.9999___
>very good goy yes yessssssss
______9.99999__
______9.999999_
______9.9999999. . .
>thats right goy yes,mmm

______9._______
_____99._______
____999._______
>oi vey what is this goy doing...
___9999._______
>SHUT IT DOWN
__99999._______
>SHUT IT DOWN EZEKIAL ITS GONNA BE ANUDDA-
_999999._______
>OY VEY IYS ANUDDA SHOAH
9999999. . .
>אֵל מָלֵא רַחֲמִים שׁוֹכֵן בַּמְּרוֹמִים, הַמְצֵא מְנוּחָה נְכוֹנָה עַל כַּנְפֵי הַשְּׁכִינָה, בְּמַעֲלוֹת קְדוֹשִׁים וטְהוֹרִים כְּזוֹהַר הָרָקִיע מַזְהִירִים אֶת כָּל הַנְּשָׁמוֹת שֶׁל שֵׁשֶׁת מִילְיוֹנֵי הַיְּהוּדִים, חַלְלֵי הַשּׁוֹאָה בְּאֵירוֹפָּה, שֶׁנֶּהֶרְגוּ, שֶׁנִּשְׁחֲטוּ, שֶׁנִּשְׂרְפוּ וְשֶׁנִּסְפּוּ עַל קִדּוּשׁ הַשֵׁם, בִּידֵי הַמְרַצְּחִים הַגֶּרְמָנִים הָנַאצִים וְעוֹזְרֵיהֶם מִשְּׁאָר הֶעַמִּים. לָכֵן בַּעַל הָרַחֲמִים יַסְתִּירֵם בְּסֵתֶר כְּנָפָיו לְעוֹלָמִים, וְיִצְרוֹר בִּצְרוֹר הַחַיִּים אֶת נִשְׁמוֹתֵיהֶם, ה' הוּא נַחֲלָתָם, בְּגַן עֵדֶן תְּהֵא מְנוּחָתָם, וְיַעֶמְדוּ לְגוֹרָלָם לְקֵץ הַיָּמִין, וְנֹאמַר אָמֵן.

>>9750556
> [math]\frac{\bar{9}}{1\bar{0}}[/math]
> l-lateks mann...

>>9749947
The logic of mathletecians is that they dont have to abide by physical restrictions and real rules and may have arbitrary unlimited accuracy. So your example doesn't follow.

>>9750581
>trying this hard

>>9750607
what's so difficult?

>>9750607
>yfw you actually thought the reals were complete

>>9749202
I ignore your shitposts usually but you're really dumb, man. You don't understand how to manipulate math as a language.

...99999 has a value of infinity
...11111 also has a value of infinity
...99999/...11111=9
therefore
infinity/infinity=9

>>9750539
No they aren't. 1/3 is a value but not a decimal representation.

>>9750717
not him but youve lost me anon
you are aware that if [math] \lim\limits_{x\to a}\mathrm{f}(x)=\ell [/math], then [math] \lim\limits_{x\to a}c\mathrm{f}(x)=c\ell [/math], right?

>>9750812
>...99999/...11111=9
Wrong, it's indeterminate.

Just making a contribution
In the realm of decadic numbers
[math]...99999999=-1[/math]
another rule of 10-adics is their reverse is their negative.
[math]0.3333... = 1/3[/math] and [math] ...3334 = 2/3 , \,...3333=-1/3 [/math]
so if we reverse ...9999 we see that 0.999... , in a sense, equals one.

>>9744624
my god you're dumb

0.1 / 0.9 = 0.111...
0.11 / 0.99 = 0.111...
0.111 / 0.999 = 0.111...
0.1111 / 0.9999 = 0.111...
0.11111 / 0.99999 = 0.111...
0.111111 / 0.999999 = 0.111...

0.111... / 0.999... = 0.111...
0.111... / 1.0 = 0.111...

>>9751240
[math]\frac{1}{10} ÷ \frac{9}{10} = \frac{1}{9} \\ \frac{11}{100} ÷ \frac{99}{100} = \frac{1}{9} \\ \frac{ \bar{1} }{ 1 \bar{0} } ÷ \frac{ \bar{9} }{ 1 \bar{0} } = \frac{1}{9}[/math]

>>9742117
Oh I get it
We're using latex to write these equations

>>9750973
lmao it's like you don't even do math

>>9751244
last line has inf/inf, undefined
infinity is, if nothing else, unbounded
can't let the numerator lose
can't let the denominator lose
Can't even let them have a tie

undefined

>>9750717
anon, the identity you posted in your image (i'm guessing you're too brainlet to latex properly) is exactly what I used to justify my derivation. The limit of a constant multiple is the constant multiple of the limit, to put >>9750962 into words.
Please tell me you knew this and you were just trolling, this is week 2 of calculus.
[eqn]\lim_{k \rightarrow \infty} \frac{9}{10} \frac{1-\frac{1}{10^k}}{1-\frac{1}{10}} = \frac{9}{10}\cdot \frac{1}{1-\frac{1}{10}} \cdot \lim_{k \rightarrow \infty}\left(1-\frac{1}{10^k}\right) = \frac{9}{10} \cdot \frac{1}{\frac{9}{10}} = 1 [/eqn]
Brush up on your arithmetic before you post next time, you've made a fool of yourself.

>>9751600
>1 - 0 = 1 therefore thusly ergo me ams smart and haved sumseccsfully used limit

[math]\lim_{k \rightarrow \infty} \frac{1}{10^k} = \frac{1}{10^\infty} = \frac{1}{\infty} = 0[/math]

>>9751734
Why those extra steps? The limit is trivial.

>>9751734
[eqn] \lim_{k\rightarrow\infty}\left(1-\frac{1}{10^k}\right) = \lim_{k \rightarrow \infty}1 -\lim_{k\rightarrow\infty}\frac{1}{10^k} = 1 - 0 = 1 [/eqn]
I spelled it out explicitly for you this time, the earlier limits are of course trivial given this fact.

>>9751765
>1 - 0 = 1

>>9751881
Correct, that's not very interesting in itself. I just laid out the easier steps for you since your phenotype was insufficient to understand my initial post. Of course it's trivial that [math] 0.\bar{9} = 1 [/math], but since brainlets like yourself feel the need to contest it I gave an explicit derivation from the definition.

>>9743135
>Or just write it in base 3
but writing it in base 3 is redundant. OPs question is expressed in the base 10. In a base 10 system it is an infinite number. Using a base of any multiple of 3 leaves you with complete numbers not endless approximations. 3/3 can be applied to any numerical based system to equal any number you please but again op asked specifically in base 10 so why would we answer the question in a non related numerical system. May as well just answer in another language as well since were ignoring the substance in OP's post.

>>9751765
Is it possible to express a function as series? and any other way rather than classic f(x) etc.... sorry some of you might say its a bloody stupid question....