/sci/ - Science & Math

>>11669397
>so setting y=0.999... would yield a value of x that is infinitesimally close to pi but not pi
This requires the assumption that 0.999... =/= 1, making your argument circular

>>11669397
3 < π
3.1 < π
3.14 < π
3.141 < π
3.1415 < π
3.14159 < π
3.141592 < π
this continues endlessly
π < π

>>11669549
see
>>11669569
y=-cos(3)=0.989992496600445457271572794731261302393679096615588328814...
y=-cos(3.1)=0.999135150273279464492376054541466262836641669947942743544...
y=-cos(3.14)=0.999998731727539545285114306345049983854508439392120932039...
y=-cos(3.141)=0.999999824380866392940839580833975469489338051607740815449...
y=-cos(3.1415)=0.999999995707656152283851309987064521145887541258770243337...
y=-cos(3.14159)=0.99999999999647923060461239250850048325101828738865122795...
y=-cos(3.141592)=0.99999999999978641019108725942917886921117573907654096975...

y=1 if and only if x=pi ... exactly

>>11669645
Are you retarded? Did you miss the fact that it approaches 1 as the argument approaches pi?

>>11669397
Super EZ proof that 0.999... = 1
1/3 = 0.333...
3 x (1/3) = 3 x 0.333...
1 = 0.999...

>>11669645
Yes and if 0.999... = 1 then arccos(0.999...) = pi exactly. Which it does, so it does.

>>11669569
if you proved pi < pi we have bigger issues than 0.99.. not being 1

>>11669397
SAGED

>>11669826
cool image, but "by induction"...? didn't get that

>>11669837
You've got a lot of reading to do.
I'll even give you your first link: https://en.wikipedia.org/wiki/Mathematical_induction

>>11669855
You're only proving one case. I don't know what you think induction is, but that isn't it.

>>11669397
I can disprove that theorm by make the observation that 0.99... and 1 are not the same numbers. mathtards btfo

>>11670753
do it big boi

>>11670834
I-i...I just did?

>>11670847
I make the observation that you're an idiot.
>wow it really works

>>11669826
>You might think every number has a unique decimal expansion. You would be wrong
the absolute lack of argument - made only worse by the fact that the image clearly contains actual arguments and thus would include support for this claim if it could - only strengthens my suspicions that the 0.999... fags are on to something

these threads will continue to be posted until /sci/ actually learns mathematics and produces a satisfying explanation.

[math]
\boxed{0 < p < 1} \\
1 = p + (1-p) ~~~~~~ \overset{1}{ \overbrace{[=====p=====|==(1-p)==]}} \\
\text{divide p using x} ~~~~~~ \overset{1}{ \overbrace{ \underset{p}{[ \underbrace{=====x=====|==(p-x)==}]} ~~ + ~~ (1-p)}} \\
\\
\text{solve x and (p-x), when length ratios must be the same} \\
\dfrac{x}{p-x}= \dfrac{p}{1-p} \Rightarrow x- xp = p^2 - xp \Rightarrow \underline{x=p^2} \Rightarrow \underline{(p-x)=p(1-p)} \\
\overset{1}{ \overbrace{ \underset{p}{[ \underbrace{=====p^2=====|==p(1-p)==}]} ~~ + ~~ (1-p)}} \\
\\
\overset{1}{ \overbrace{ \underset{p^2}{[ \underbrace{=====p^3=====|==p^2(1-p)==}]} ~~+ p(1-p)+(1-p)}} \\
\overset{1}{ \overbrace{ \underset{p^3}{[ \underbrace{=====p^4=====|==p^3(1-p)==}]} ~~+ p^2(1-p)+p(1-p)+(1-p)}} \\
(1-p)+p(1-p)+p^2(1-p)+p^3(1-p)+ \cdots =1 ~~~~ \left | ~ \times \frac{1}{1-p} \right . \\
1+p+p^2+p^3+ \cdots = \dfrac{1}{1-p}
[/math]

>>11669826
TEH MATH.

CRINGE. I imagine a fat slob who loves anime and does math to feel cool.

>>11670853
Nice b8

>>11670889
what is this math even
written so neatly i have never seen such style before

>>11669397
>Guys I proved that A =/= A
Learn2definition

>>11671018
lol retard it clear says there in the op that B =/= A
what are you literally brain damaged?

>>11669397
pi = lim(n->inf) (cos(360/n) * n)/2

>>11671031
sorry, replace cos with sin

>>11669685
I'm not approaching 1 I am approaching 0.999... which is an infinitesimal step below 1.
>>11669797
x=arccos(-y)
let us see the iterations as y approaches 0.999... not 1.
x=arccos(-0.9999999)=3.141145439990566500477009347399887558935717056958176735465...
x=arccos(-0.99999999)=3.141451232233438077827300291442614303329194482853121225407...
x=arccos(-0.999999999)=3.141547932230239515888751861631142431400718260085750433840...
x=arccos(-0.9999999999)=3.141578511454169389661025165982689624213851967799185604816...
x=arccos(-0.99999999999)=3.141588181453838235156470602424130672713759902775571409191...
x=arccos(-0.999999999999)=3.141591239376230865249743451392994237261322265928440484832...
x=arccos(-0.9999999999999)=3.141592206376197738500977321482269404595357865558939211351...

where the exact number pi = 3.14159265358979323846264338327950288419716939937510...

looking at it logically, each 9 appended to the number 0.999... adds a greater deal of accuracy to the number pi.

relatively speaking (looking at the last arccos iteration), it takes about 19 9's to get 6 correct decimal digits of pi, which isn't very fair. If the resolution of 0.999... is not proportional to the resolution of pi in the limit, then it means that the ideal realization of pi with "catch up" later to all of those 9's appended in the limit or even never.

tldr it takes a lot of 9's to make pi, therefore each digit of pi has some amount of (9/10)^n in the function that help build it.

to make it clear i am not approaching 1 I am approaching 0.999... in the limit.

>>11669782
>>11670847
>>11671018
sqrt of minus one (0.000...1) equals minus one

>>11671125
so the square root of minus one (0.000...1) = minus one (0.000...1) cause placeholder 0 and negative numbers do not exist

Zero (0) is simply Shorthand for Minus One (0.000...1) and for Infinity (∞) because Both are exactly Equal completing the Definition of so-called 'undefined'.

>>11671039
devil

>>11671280
cos every1 is a sinner

Here's a simple argument why 0.99... != 1

If two numbers a and b are the same, then clearly for any function f, we must have that f(a) = f(b). This is just common sense.

Define f to take in any real number, and return the digit in the tenths place.

Then f(1) = 0, but f(0.999...) = 9. Therefore 0.999... != 1.

>>11671425
american education, folks

>>11670984
https://youtu.be/XFDM1ip5HdU?t=4m50s

>>11671471

0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...

...9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...

...999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...

...99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...


WHERE'S THE FUCKING ONE, THEN?

>>11671515
>>11671519
>>11671522
>>11671525
>let's pretend finite is infinite

>>11671525
up your ass

>>11671545
I could do it until the end of time and there would still be no 1 faggot.

>>11671563
oh sweetie, that's why inf isn't a number

>>11671101
One of the most basic properties of the real numbers is the Archimedean property, part of which states that there are no infinitesimally small real numbers. More exactly, it states that for all real numbers greater than zero, there are natural numbers n such that 1/n is less than the real number.
This is provable from an even more fundamental property of the reals, the least upper bound property. It states that any nonempty set of real numbers which is bounded above has a least upper bound: a number which is >= all elements of the set, and <= all upper bounds of the set.
Let S be the set of infinitesimals in the reals. S is obviously bounded above by 1, because there wouldn't be infinitesimals greater than one. Then, assume by contradiction that S is nonempty. This means that S has a least upper bound I'll call r.
r < 2r, and since r is an upper bound, 2r cannot be in S, so can't be infinitesimal. Thus, we can pick a natural n such that 1/n < 2r.
r/2 < r, and since r is the least upper bound, there must be at least one infinitesimal i > r/2.
However, 1/(4n) < r/2 < i, meaning i is not infinitesimal. By contradiction, S is empty.

>>11671425
Let f be the function that returns the denominator of any fraction. f(1/2)=2, but f(2/4)=4. Thus, 1/2 != 2/4.

>>11671571
At no point during an eternity is there even the mechanism for a 1 to appear.

Face it mathcuck, you've been hoodwinked into believing illogical fantasies.

>>11671614
6/3
Where's the 2?

>>11669826
x = 0.333...
10x= 3.333...
10x-x = 3.333... - 0.333...
9x = 3
3x = 1
x = 1/3 = 0.333...
BUT
x = 0.33oh wait you just realized that the "proof by induction" presented in your picture is fucking retarded and is just an aberration of humans using decimal to represent numbers being unable to deal with that situation very well333...

>>11671614
>during an eternity
>during
lol, what on earth is going on in that pretty little head of yours

>>11671618
6/3 is calculation, not a number

0.9999... is a numerical expression

>>11671661
eternity by definition lasts forever. Are you dumb?

>>11671477
very neat

>>11671563
i could write pi forever and still not be able to make a perfect circle out of it

perfect circles must be mathematically impossible

>>11671717
6/3 is a number, just like 1+1 is a number, 0.5 is a number 7*2 is a number, and the infinite sum from n=1 to infinity of 9/(10n) is a number. It doesn't matter how you label something, as long as it equals a number, it is a number.

>>11671726
This is literally correct. Perfect circles are mathematically impossible.

>>11669397
why do people still comment on these threads?

>>11669397
you just -said- that it's not the case. but it in fact is true that 0.999...=1=-cos(pi).

>>11671717
>by definition
ok, here's an actual definition:
https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity that is greater than every real number.

nothing about 'time', nimrod

>>11671784
x^2+y^2=r^2
>wipes sweat off forehead

>>11671929
Nice irrational set you have there. Shame you can't enumerate it.
Just tell me you're a midwit next time, things will be a lot quicker.

>>11671979
>enumerate it
only losers like you need to do that.
it's perfect, cope

>>11671997
It's not real if you can't yield it.

>>11669397
You are absolutely correct OP, nice proof this shows proof that you have a creative mind.

Also it's kind of wierd that this is the exact way that I thought of the .999 problem.

>>11672265
OP here.
are you... me?

>>11669397
>so setting y=0.999... would yield a value of x that is infinitesimally close to pi but not pi
you assumed that .999... = 1 so this is a non sequitor

why do these threads survive lol