Brainlet.png

1 = 0.99999....

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why do you disagree with it?

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

therefore 1 = 0.999... + infinitesimal aka hyperreals

get fucked

wrong

>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

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

you are the true brainlet here.

you don't understand what repeating digits actually mean.

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

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.

>9/9 = 0.9...
wew

...

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.

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

Bad post.
Read

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.

[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]

[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]

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

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.

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

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

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

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

basically yes

infinities are nonsensical in reality

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.

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

> math is real world
KEK

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

brainlet

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

axiom: infinitesimal = 0.

>infinitesimal = 0
wrong

the funniest was when he claimed the Hilbert hotel was gay

1 = 4/4
1/4 = 0.255555555555
1/4 * 4/1 = 4/4
1= 1.02222222222

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?

youtube.com/watch?v=r5DHquP1HWU

HOW THIS HELP BUNGO SURVIVE?

BUNGO NEED NOT KNOW THIS

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

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.

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

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

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

hyperreals are not real

am i using the calculator like a pro?

>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

1/3 = 0.33333333

thats not the way to prove it.

>let

tfw i recognize him

>what is an infinite series

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

not true

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

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

>if