Does this concept trigger your autism, Veeky Forums?

Does this concept trigger your autism, Veeky Forums?

Other urls found in this thread:

wolframalpha.com/input/?i=1/3 - 0.3...
wolframalpha.com/input/?i=inf+1
en.wikipedia.org/wiki/Zeno's_paradoxes#Achilles_and_the_tortoise
youtu.be/wf2P8SnOwLo?t=1m10s
twitter.com/SFWRedditImages

No, the precise meaning if convergance is perfectly expresible in formal mathematical languange.

[math]
1 = \dfrac{3}{3} = 3 \cdot \dfrac{1}{3} = 3 \cdot 0.\bar{3} = 0.\bar{9}
[/math]

Retard

wolframalpha.com/input/?i=1/3 - 0.3...

asshole

hello shitlatexman

You mad a mistake
[math]\dfrac{1}{3} \neq 0.\bar{3}[/math]

...

bro it's literally basic analysis why the fuck does this trigger you???? once you have a rigorous understanding of the reals this should be very obvious

you can't even spell correctly

*You

fuck off back to

But if .99999 = 1 then why doesn't .333333 = .333334

Can you give me an instance where it matters?

It's no longer repeating then.

>the moron doesn't put in the "..."
because 9 is the largest digit

Well I guess we don't know what 0.999999... is, so let's set it to an unknown:
[eqn]N = 0.999999...\\
10N = 9.999999...\\
10N - N = 9.999999... - 0.999999...\\
9N = 9\\
N = 1[/eqn]

begging the question

what question?

Learn to carry, brainlet.
Your retard math implies 0.9 × 10 = 9.9

>wolfram

What is 1÷3?

Is it 0.3? No?
Is it 0.33? No?
Is it 0.333? No?
Is it 0.3333? No?
Is it 0.33333? No?
Is it 0.333333? No?
Is it 0.3333333? No?
Is it 0.33333333? No?
Is it 0.333333333? No?
Is it 0.3333333333? No?
Is it 0.33333333333? No?
Is it 0.333333333333? No?
Is it 0.3333333333333? No?
Is it 0.33333333333333? No?
Is it 0.333333333333333? No?
Is it 0.3333333333333333? No?

What is 1÷3?
3 goes into 1 no times, but 3 goes into 10 three times with 1 left over
0.3
3 goes into 1 no times, but 3 goes into 10 three times with 1 left over
0.33
3 goes into 1 no times, but 3 goes into 10 three times with 1 left over
0.333
3 goes into 1 no times, but 3 goes into 10 three times with 1 left over
0.3333

Hmmm....

so no matter how many times you derive an extra 3 in the significand, you'll always have remainder 1? So simply saying "repeating 3's" is not sufficient in describing the number?
If only there were a sufficient way of describing remainder 1....

Oh! I got it.
1÷3 = 0.3r1
0.3r1 × 3 = 0.9r3
3 goes into 3 one time, no remainder carry up!
0.3r1 × 3 = 0.9[+1]r0
0.3r1 × 3 = 1.0!

But remember, 0.3r1 > 0.333...
And of course, never forget infinity is not a number, so "an infinite amount of 3's" has no intelligible meaning :^)

>0.999... is equal to 1
>0.0000...1 is NOT equal to 0 at the same time

Repeating decimals are not simply reapeating without meaning. They are always by definition a standin for a rational number that could be written a different way. So then the question is which raional number does .999... or .333... represent ?

who knew, infinite is different than finite

1/3=0.333...

You are reading too far into repeating decimals bro.
They exist simply as a byproduct of concatenating long division, but designed by retards who never figured it'd make more sense to write the remainder instead.

Infinite is, by definition, unachieveable

women are unachievable to you
and yet they exist

0.9 / 10 = 0.09
0.99 / 10 = 0.099
0.999 / 10 = 0.0999
0.9999 / 10 = 0.09999
How many 9's would you like to extend this to?

ok genius,
is 9.999.../10
=1 , 1 ?

I'm sure you have good reason to believe I'm a virgin, right?
Totally not an invalid assumption, right?
Surely your interpretation of infinity couldn't be an invalid assumption, right?

Ah i'm kidding of course i know you're a retarf full of invalid assumptions. Don't need you to verify it.

>unachieveable
uh-huh
yet achilles catches up with the tortoise, easily

>I'm a virgin, right
not necessarily, cows exist

9.9 / 10 = 0.99
9.99 / 10 = 0.999
9.999 / 10 = 0.9999
9.9999 / 10 = 0.99999
How many 9's would you like to extend this to?

>tries writing a 1 after the process of writing an infinity of 0s

moron

Achilles never catches the tortoise without finite time or finite distance. Are you really so much of a brainlet to have never understood zeno's achilles paradox was littered with finitist elements?

>after
>infinity

that's my point?

infinite, ty

so... shifting works.

Nonono, you cant complete infinity so it doesnt matter, anything could come after it.

no, nothing comes after it, except more infinity, that's the point of infinity

lrn2read numbnut

9.(infinity 9's) / 10 = 0.(infinity+1 9's)

Uh oh it looks like you fuckered up boyo, aren't you not allowed to have "infinity+1"?

How are you gonna explain this one?

wolframalpha.com/input/?i=inf+1

>nothing comes after infinity
Which is only a valid statement if you reached infinity to know it.

You can't make any confident assumptions about what could be after infinity, you'll never make it to infinity in the first place. Much like you'll never make it to heaven.

Thats not how numbers work hombre.

kek
I'll just let Wolfram-Alpha and you battle it out.

but since you can't reach infinity in the first place, why would you assume there's an "after", that makes no sense

You don't know if something can exist after infinity because you cannot reach infinity. One way or the other it is no more more valid to assume nothing of value could exist there, or if only the most important value could exist there.


But really what we're saying is, because infinity is unreacheable, there cannot br a number 0.(infinite 9's) that could require a number 0.(infinite 0's)1 to exist.
Since infinity is never reached but a large finite number will always exist by attempting, that must simply mean there can only exist a large finite number of 9's in 0.999...

the fact it's unreachable is irrelevant, we can still make use of it through abstractions

Abstract sounds like codeword for makin up gay retarded fantasy bullshit cause real elements are too taxing for brainlets to obey rules and abide by logic :o

abstraction is a higher level brain function, sorry i didn't realize i was talking to a retarded monkey

Honestly you couldn't have said it more retarded if you tried. You really went straight for the godmode didn't you? Couldn't have just said it was useful, nope - straight to spilling your spaghetti by associating it with supreme intelligence.

What a fuckin goober you are. I'll be forward, i'm not interested in roleplaying with you so just cut the powercreeping right here, k?

>went straight for the godmode
that works fine with infinity

I can abstractly count to infinity and then abstractly count higher than infinity. Whats you argument now.
Infinity+1 makes sense if you just think abstractly.

if you're gonna badmouth the concept of abstracting without understanding that we couldn't be having this conversation without it, you deserve all the insults

Forgive me, i missed the part where we were having a conversation about an abstract concept cause i was too busy insulting you calling you a retard. Maybe we are only having a conversation abstractly in your head along with the rest of your completely invalid assumptions about life.

yeah, alzheimer's will do that to you, you should get checked out

...

>Achilles never catches the tortoise
KEK

>Infinity+1 makes sense
sure, inf+1=inf, no problem

The tortoise moves at half the speed of achilles
Achilles gives the tortoise a head start of x seconds in a race
Achilles reaches the tortoise after 2x seconds have passed.

X = any finite number: not infinite
X = infinite: achilles never even begins chasing after the tortoise

Thats not how numbers work, hombre

>so much butthurt he can't contain it
nice one kid, better whip out another meme pic so you can feel better about yourself

Would it kill you to shut the fuck up?

Read for yourself
en.wikipedia.org/wiki/Zeno's_paradoxes#Achilles_and_the_tortoise

If you don't want to talk about A&T, just say so

...

No.
In fact, it makes perfect sense for anyone who studied 10th grade math.

>who is it talking to

I just described the problem to you.

no, you invented your own story and for some reason call it A&T

why risk it?

youtu.be/wf2P8SnOwLo?t=1m10s

Do you guys never get tired?

every 0.999... a while

if (0.999... =/= 1), then there must exist a number n such that (0.999... < n < 1)

[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]

For you people who can't "believe" the math:
If 0.9999... < 1 then you admit that there is a number N = 1 - 0.9999.... = 0.000....0001 that:
>Has an infinite amount of zeros (because there is an infinite amount of 9).
>But it has to end with 1.
These two points contradict themselves so it can't be true (a number of infinite digits can't have a "last" digit, just like there is no "last" digit in pi, or e).

>These two points contradict themselves
hurr what is ordinal arithmetic

The concept is not contradictory.

How is it not?

where do you put the closing brace for an infinite set?

If
[math]1=0.\overline{9}[/math]
Then
[math]1-0.\overline{0}1=0.\overline{9}=1[/math]
And
[math]0.\overline{0}1=0[/math]
[math]0.\overline{0}1 + 0.\overline{0}1=0.\overline{0}2[/math]
[math]0=0.\overline{0}2[/math]
Therefore all numbers are equal to zero
>this is what 0.99...=1 retards actually believe

what is your major?

fuck off back to

Feminist economics

oh shitlatexman, never change

>if (0.999... =/= 1), then there must exist a number n such that (0.999... < n < 1)
.9999
.99999
.999999
.9999999
.99999999
.....
.9999999999999999
.99999999999999999
.999999999999999999
.9999999999999999999
......
.999999999999999999999999999
.9999999999999999999999999999
.99999999999999999999999999999

The concept of infinitely repeating is that there will never be a shortage of larger expressions of that ^^^ pattern.

....

...
.9999999999999999999999999999999999999
.99999999999999999999999999999999999999

.....

.....

.....

1
Its not that .999999...(repeating infinitely) = 1

Its that there may be a problem with the concept of infinite repeating.

To try to bring it into physicality to have some grasp at an understandable example:

Imagine you had some marbles: 12 to be exact.

And you take one of them. And you cut it in half. .5 of a marble right.

Ok you throw that one away.

You take another marble. That marble = 1 right?

You take a little "the sharpest blade in the world" and you scrap off the marble:
.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

marble material.

Or ok... lets say you remove 1 atom.. or ok... 1 electron from the marble.

It is still 1 marble.

But it is technically less than the absolute wholeness it was prior to the removal of any speck.

This gets into semantics I guess, like that how many grains of sand until it can be called a pile or heap?

How many atoms do you remove from a marble before you can no longer consider it a marble, or 1 marble?

Is a marbl cut inhalf considered a marble?

>incoherent rambling and hand waving intensifies

>not an argument fizzles into out as itself before it ends to begin

If
0.999...8 != 1
Then there must be a number n such that
(0.999...8 < n < 1)
If repeat this enough times we eventually come to the conclusion
0.9 = 1

>if (0.999... =/= 1), then there must exist a number n such that (0.999... < n < 1)
.9999
.99999
.999999
.9999999
.99999999
.....
.9999999999999999
.99999999999999999
.999999999999999999
.9999999999999999999
......
.999999999999999999999999999
.9999999999999999999999999999
.99999999999999999999999999999

The concept of infinitely repeating is that there will never be a shortage of larger expressions of that ^^^ pattern.

....

...
.9999999999999999999999999999999999999
.99999999999999999999999999999999999999

.....

.....

.....

1
Its not that .999999...(repeating infinitely) = 1

Its that there may be a problem with the concept of infinite repeating.

To try to bring it into physicality to have some grasp at an understandable example:

Imagine you had some marbles: 12 to be exact.

And you take one of them. And you cut it in half. .5 of a marble right.

Ok you throw that one away.

You take another marble. That marble = 1 right?

You take a little "the sharpest blade in the world" and you scrap off the marble:
.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001

marble material.

Or ok... lets say you remove 1 atom.. or ok... 1 electron from the marble.

It is still 1 marble.

But it is technically less than the absolute wholeness it was prior to the removal of any speck.

This gets into semantics I guess, like that how many grains of sand until it can be called a pile or heap?

How many atoms do you remove from a marble before you can no longer consider it a marble, or 1 marble?

Is a marbl cut inhalf considered a marble?

>before it ends to begin
i rest my case

try again, with capital letters

you've literally gone marbles

The number 1 is a whole 'thing', and it can be divided into parts, it is composed of parts.

An object, baseball, tomato, apple, tree, cup, is a whole thing, that can be divided into parts, and is composed of parts.


There are 3 apples on the table.

Each apple is 1.

Except objects are not composed of infinite parts, as The Perfect Objects That Are Abstract Numbers are claimed to be...

If a number is composed of infinite parts... that means you can remove 1 piece from the number, infinitely, and never lessen the number?

That would be like taking infinite atoms away from an apple and still having a whole apple?

The system of numbers is a system of conviennce, and of perfect sense and proportion and order: and works perfectly (in most if not absolutely almost all areas), but gets a little sketchy with these 'seemingly' partially invented rule conceptions: like there are infinite quantities between any 2.

The rules apparently beg this to be the case, and at the same time logic appears to say something is very strange about this.

Because it is not real, and tangible, so much of the mapping, the conception and use of math works so well with what is real, and so much of it transposes so smoothly to the real (like 1 number 1. 1 apple. cut number 1 in half, get . 5 of number 1. cut apple in half get .5 of 1 apple)

but as you can find an apple and show me, I think it is a bit harder to go into nature and show me a .999999... infinitely repeating. You can find me 9 apples. and 999 apples. But good luck finding 999999999... infinitely repeating apples.

You can find me .999999999999999 apple: remove an electron from an apple.

But what would it mean to remove .999999....(infinitely repeating) from an apple?

Shave off a sliver of an electron? (if that were possible)

Shave off .9999999999999 of an electron?

Figuratively or literally? Indeed the limit is 1, however this should not be taken to imply that "approaching a certain point but never reaching it" means "actually reaching that point"?

THE CONCEPT PORTRAYED IN THE OP IS LITERALLY THE INVENTED (BECAUSE I FEEL LIKE IT) ¯\_(ツ)_/¯ CONCEPT OF ROUNDING UP, BUT WITH AN EXTRA STEP OF PRETENDING YOU DIDNT

>Veeky Forums confuses the modern numerical system with reality
It is a common mistake. Our decimal and arithmatic systems are functional but not always ideal.

matmaticians forget that physics has minimums such as the planck length and its implications with the speed of light and quantitization of energy. But math fags are too autistic to acknowledge.

>however this should not be taken to imply that "approaching a certain point but never reaching it" means "actually reaching that point"?
in fact the real numbers collapse this distinction, which is otherwise sensible