brainlet.png

[Anonymous No.9553072]

1 = 0.99999....

[Anonymous No.9553110]

why do you disagree with it?

[Anonymous No.9553142]

>>9553110
1 = 0.9 + 0.1 = 0.99 + 0.01 = 0.999 + 0.001, etc

therefore 1 = 0.999... + infinitesimal aka hyperreals

get fucked

[Anonymous No.9553174]

>>9553142
wrong

[Anonymous No.9553199]

>>9553072
>le asumme 0.9999... =/= 1
>clearly 0.99999... is smaller than 1
>now there le exists a number between 0.99999... and 1
>let (le disgruntled disapproving cat face.jaypeygee xD) x be any decimal number between 0 and 1
>clearly (WHY?) there exists no decimal number that fits between 0.9999... and 1
>therefore our assumption was wrong and 0.9999 = 1

There you go boys, please share, like and subscribe

[Anonymous No.9553288]

>>9553142
x = 0.999...
10x = 9.999...
9x = 9
x = 1
1 = 0.999...

you are the true brainlet here.

[Anonymous No.9553326]

>>9553142
you don't understand what repeating digits actually mean.

[Anonymous No.9553340]

>>9553072
>people are literally too stupid to follow grade school arithmetic
>cover this up by pretending 0.999... "really" equals 1

[Anonymous No.9553358]

Let {xn} be an infinite sequence of the decimal expansion of 0.99... where n=1 implies x=0.9 and n=2 implies x=0.99 et cetera.

For all e>0 there is some number N such that
n>=N implies |xn - 1| < e.

Thus, 0.999... = 1 since 0.999... may get arbitrarily close to 1.

[Anonymous No.9553380]

>>9553340
>9/9 = 0.9...
wew

[Anonymous No.9553394]

Does 0.333... equal 1/3? I guess, not. Crisis averted.

[Anonymous No.9553397]

0.999... is not 1

There cannot ever exist an infinite amount to have been fully counted to completion, thus there cannot ever exist an infinite amount, thus any arbatrarily large amount must be finite, and any arbatrarily large finite real number amount can be bounded by proper rules not abused by brainlets.
0.999... itself makes no sense unless you imply the 3 dots have a static, constant definition, else you're required to supply how much decimal accuracy you're going for.

X= 0.999...
10X = 9.99...
10X-X = 8.99...1
9X = 8.99...1
9X/9 = 0.999...
This is how normal people do normal that that actually matters

What is 1 ÷ 3?
Well 3 goes into 1 zero times
0.
But 3 goes into 10 three times
0.3
with one leftover, bring down a zero, into ten
0.33
With one leftover... bring down a zero, into a ten
0.333
With one left over....
0.3333
With one left over......
0.333333333
No matter how many 3's exist in this decimal, it will never fully equate the decimal value of [math]\frac{1}{3}[/math], so in reality [math]0.\bar{3} < \frac{1}{3}[/math], multiply it by 3, [math]0.\bar{9} < 1[/math]

[Anonymous No.9553410]

>>9553397
>

There cannot ever exist an infinite amount to have been fully counted to completion, thus there cannot ever exist an infinite amount, thus any arbatrarily large amount must be finite,
What does its 'existence' has to do with anything? Does 1/2 exist? Does -1 exist? Does sqrt(-1) exist? Does 10^10^10^10^10^10 'exist'?
Your argument is nonsensical.

[Anonymous No.9553411]

>>9553340
How did you never learn long division?

[Anonymous No.9553421]

>>9553410
Fuck yourself, its my birthday and new years day today. Not spending it arguing with a fucking mongoloid who has to aytenpt invalidating existence in entirety just to justify using infinity as a number.

Honestly, you're just too dumb. Attend a university or something. Feel shame for how stupid you are. Just go be something that eventually leads to a proactive approach to improving your life from utter insignificance.

[Anonymous No.9553463]

>>9553397
>>9553421
holy shit this person is a brainlet

[Anonymous No.9553482]

>>9553174
actually it's correct, that's how hyperreals work dumbass

>>9553288
wow nice proof which 3rd grade teacher taught you that?

>>9553326
t. brainlet

yes neither does Terence Tao or leibniz or abraham robinson... yep you're a genius

[Anonymous No.9553484]

>>9553411
Of course I did, but I'm not the one claiming 1=0.999...

[Anonymous No.9553514]

>>9553463
(You) are dumb.

[Anonymous No.9553525]

>>9553326
It means they never end, but math requires finiteness to produce a finite result, so an invocation of a repeating decimal must have a finite amount of digits in the significand. Thats just how math works.

0.999... < 0.9999... < 1 is the simplest way to think about it. There will always exist a number between 0.999... and 1 that at least is 0.999... with one more 9 in it. You could say there are infinitely many 0.999+(n nines) between 0.999... and 1

[Anonymous No.9553534]

>>9553340

[Anonymous No.9553582]

>>9553142
You can't just show us a trend and say that's a proof, idiot. You probably only read the wikipedia page for hyperreals, so you're not really qualified to talk about it.

[Anonymous No.9553588]

>>9553534
>I'm Kent Mansley and I work for the government.

[Anonymous No.9553602]

>>9553525
Bad post.
Read
>>9553199

[Anonymous No.9553947]

>>9553602
Retard post, 0.999... has no consistent value in your example. You disregard the fact that an infinite amount cannot exist relative to numeration, so there must always be an arbitrarily large real finite amount of 9's in any invocation of the number 0.999...
For example, if it were 1000 9's, there exists a value 0.(1001 9's) that is greater than 0.(1000 9's) and less than 1, and still 1 greater than that, and that, and that, and so on. It never ends. Infinity is bigger than you can imagine, and if you imagine infinity has an end, you're a lazy brainlet and don't understand what infinity is.

[Anonymous No.9553966]

[math]
\displaystyle \sum_{n=1}^{\infty}\frac{9}{10^n} = \frac{9}{10} + \frac{9}{100} +\frac{9}{1000} + ...
= b = \frac{1}{10}(9 + \frac{9}{10} + \frac{9}{100} +...)
= \frac{1}{10}(9+b) = b \\
\frac{1}{10}(9+b) = b \\
\frac{9}{10} = \frac{9}{10}b \\
1 = b
[/math]

[Anonymous No.9553972]

[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]

[Anonymous No.9553977]

>>9553966
>t. Never learned how to carry numbers and pay attention to decimal location and also dumb enough to believe infinity is a numerical value

[Anonymous No.9553986]

>>9553525
think of it this way
is .999... a rational number?
if your answer is yes, then very simply, it equals 1.
if your answer is no, then you'll have to explain how a repeating decimal can be irrational.

[Anonymous No.9553988]

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

[Anonymous No.9553994]

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

[Anonymous No.9553995]

>>9553072
For all purposes that is true. NASA got to the moon with 5 dp. Rounding works cvck.

[Anonymous No.9554002]

>>9553582
yes i can and i just did and that's the literal idea behind non-standard analysis

[Anonymous No.9554010]

>>9553397
>pi is a cia conspiracy because you cannot write all of its decimals

[Anonymous No.9554012]

>>9554010
basically yes

infinities are nonsensical in reality

[Anonymous No.9554014]

>>9553142
hyperreals are a stupid concept and the result of an autist's interpretation of the D E E P L Y P H I L O S O P H I C A L man-made concept infinity.
Everything is finite in the real world.

[Anonymous No.9554018]

>>9553463
he's a lunatic who hand waves in all of these retard threads

[Anonymous No.9554023]

>>9554014
> math is real world
KEK

[Anonymous No.9554028]

>>9553072
1/3 = 0.333...
3*(1/3) = 3*0.333... = 0.999... = 3/3 = 1

[Anonymous No.9554030]

>>9554023
brainlet

[Anonymous No.9554032]

>>9554014
yes terrance tao is a retard, so is leibniz, and the founders of non-standard analysis

yep all brainlets, you are a genius my dude congrats

[Anonymous No.9554034]

>>9553142
axiom: infinitesimal = 0.

[Anonymous No.9554051]

>>9554034
>infinitesimal = 0
wrong

[Anonymous No.9554053]

>>9554032
the funniest was when he claimed the Hilbert hotel was gay

[Anonymous No.9554071]

>>9554053
1 = 4/4
1/4 = 0.255555555555
1/4 * 4/1 = 4/4
1= 1.02222222222

[Anonymous No.9554079]

I have a question I need answered before I can answer OP.
If an infintesimal approaches 0 but never gets there, does it equal 0? I suppose it is so small it cannot be measured, but.. is it greater than 0?

[Anonymous No.9554081]

>>9554071
https://www.youtube.com/watch?v=r5DHquP1HWU

[Anonymous No.9554093]

>>9554079
HOW THIS HELP BUNGO SURVIVE?

BUNGO NEED NOT KNOW THIS

[Anonymous No.9554098]

>>9554079
how do you define that?
btw, .000...1 is not a number

[Anonymous No.9554104]

>>9554093
Bungo I am just a stupid brainlet.
If infinity is the biggest possible number then 1 over infinity must be the smallest possible value which implies that it is not 0.

By using my certified 105 IQ intellectual prowess, a teeny tiny value is not 0 therefore 0.999 is not 1.

[Anonymous No.9554108]

>>9554098
>0.000...1 is not a number
there's actually notation for this concept in the hyperreals

scroll down here https://en.wikipedia.org/wiki/A._H._Lightstone

[Anonymous No.9554127]

>>9554079
>If an infintesimal approaches 0 but never gets there, does it equal 0?
numbers don't approach things, in any system, ever

[Anonymous No.9554130]

>>9554108
hyperreals are not real

[Anonymous No.9554815]

am i using the calculator like a pro?

[Anonymous No.9554836]

>>9554130
>hyperreals are not real
DURRRRRRRRRR DURRRRRRRRRRRHURRRRRRRRRRRRRRRRRRRRRRR
>reals are not integers
>integers are not whole
>wholes are not natural
DURRRRRRRRRRRRRRRRRRRRRRRrrrrHURDURRRRRURUHRDURRRRRRRRRRRR

i made a custom brainlet pic just for you

[You No.9554837]

>>9553994
1/3 = 0.33333333

thats not the way to prove it.

[Anonymous No.9554839]

>>9553199
>let

[You No.9554842]

>>9554018
tfw i recognize him

[Anonymous No.9554869]

>>9553977
>what is an infinite series

[Anonymous No.9555200]

[eqn]\lim_{x\to\infty} \dfrac{1}{x} = 0[/eqn]

[Anonymous No.9555279]

>>9555200
not true

[Anonymous No.9555313]

>>9554837
no, but
IF 1/3=0.333... THEN 1= 0.999...

I can live with that, and have seen no non-shitposters claim otherwise

[Anonymous No.9555387]

>>9554104
>if