/sci/ - Science & Math

no.

T. Math Professor at Harvard

>>10007403
It is not the same, but it is equal.

>>10007403
No, one has lots of 9s, the other doesn't

>>10007403
goddamn another one of these threads

yes, 0.999... is equal to 1
this is because when you say x = y for real numbers, that means that x and y approach one another -- i.e. the difference between the two approaches 0.

if you give me some concrete number for epsilon, (e.g. .0001), i can find you a number of the form .999... that makes my expression smaller than epsilon away from 1 (e.g. for .0001, i'd just give you .99999)

another way to prove to people that this is true is through some algebraic manipulations (this is less rigorous but more intuitive for people who don't understand limits or that equality is defined the way i defined it)

e.g.

1/3 = .333...
3 * 1/3 = .999...
3/3 = 1 = .999...

>>9999999

>>10007435
No.

1/3 as a fraction contains more information than it's decimal rendition. It is technically inaccurate to say 1/3 = 0.333- because the truth is those incessant 3's are being rendered for the presence of an equally incessant remainder.
Its more intelligible to say
[math]\frac{1}{3} \approx 0.\overline{3} \\ \text{ or } \\ \frac{1}{3} > 0.\overline{3} [/math], and under this it makes perfect sense for why [math]\frac{1}{3} × 3 = 1[/math], yet 0.333- × 3 = 0.999-, since [math]\frac{1}{3} > 0.333- \\ \big[ \frac{1}{3} × 3 \big] > \big[ 0.\bar{3} × 3 \big] \\
1 > 0.\bar{9} [/math]

which you can extend maximally to [math]0.\bar{9} \approx 1 [/math] given [math]0.\bar{3} \approx \frac{1}{3}[/math], but not strictly equal.
Strictly, 0.999- is less than 1.

>>10007462
wanna know how I can tell you are a mathlet?

>>10007472
You can't tell shit, the least of which includes how dumb you are.

Stay free, NPC.

>>10007462
>>10007478
why do you feel compelled to spew cancer ideas on this board?

this some jesus freak shit also?

>>10007435
But 0.9999 + 0 is still 0.9999
How do you get to 1 by adding zero?

>>10007485
stupid argument, learn some math (or at least don't leave out the ... when you try to write .999...)

1/3 = 3.333... proves that our math is inherently incomplete. Perhaps if we had invented a pure system right from the start, mathematics might have come much farther today

>>10007538
off by 3 genius

>>10007403
Picture related

>>10007410
Yes.

t. double Fields Medal laureate

>>10007540
Or were I off by 9? A better system might have been able to answer that

>>10007547
No.

t. God (the Jewish one, yeah i'm the real one)

>>10007547
No

t. [math]\color{red}{Satan}[/math]

>>10007462
not sure if elaborate troll or never learned limits.
I'm think the latter however.

>>10007403
If it weren't, then dividing numbers wouldn't work.

>>10007966
limits aren't valid when defined with infinity, as the very idea makes it unlimited. Limits used exclusively in this manner are just bullshit trying to justify other bullshit(infinity). It's like the democratic party making lies reliant on other lies and thinking normal people care about their web of lies when everyone can just stop at the realization Trump won fair and square.

related, conversion and diversion are the same singular process and I'd be happy to show you why, and further why even if you wish to entertain the bullshit that is infinity, it's retarded to assume a difference between conversion in the affirmative and diversion in the negatory.

Alternatively, fuck off.

>>10007991
you are a jesustroll and you already got pwned in >>10007425

just cut it out and stop shilling pseudo-math, it's tiring, and you should come to grips with the fact that you're spewing cancerous horse shit that makes this board turn into a wasteland where nobody wants to read anything

>>10007546
Stop posting this bait image and learn to do math

Green doesn't know how multiplication works
> 0.99 × 10 = 9.90
> 0.[infinite 9's] × 10 = 9.[infinite-1 9's, and 0], not 9.[infinite 9's] for a total of infinite+1 9's
Brown doesn't know how division works
>1÷3 always has a remainder, thus it's result in decimal is less than the fraction 1/3, rather than having a true equality in decimal
>[math]\frac{1}{3} > 0.\bar{3}[/math]
>[math]\big[ \frac{1}{3} × 3 \big] > \big[ 0.\bar{3} × 3 \big] [/math]
>[math]\frac{3}{3} > 0.\bar{9}[/math]
Blue is just not even math and is bullshit

>>10007995
Cry more, paranoid crybaby.

>>10007403
As strings in [math]\Sigma^* \cup \Sigma^{\omega}[/math], no. As the numbers in [math]\mathbb{R}[\math] these strings represent, yes.

>>10008006
>BUT I PRESSED THE BUTTONS [1] [÷] [3] [=] ON MY CALCULATOR AND IT SAYS THE RESULT IS 0.3333333... SO IT MUST BE TRUE CAUSE UMMM, HELLLOOOO DUH I PRESSED THE [=] EQUALS BUTTON!!!! THAT MEANS EQUAL!!!!

>>10008006
1) You can either have a zero at the end of nines, or you can have infinite nines. Those are mutually exclusive. The fictional number 9[infinite-1 9's, and 0] doesn't exist. Learn some damn math.
2) 1/3 only has a remainder if you STOP. You don't STOP an infinite process you moron. So 1/3 is equal to .3 repeating.
3) Blue is actually a pathetically easy and basic application of Calculus 2 knowledge.

In summary: you know nothing, and your criticisms reflect that.

>>10008063
thank you for a sane post

>>10008063
Oh come the fuck on lmao.
>NUMBERS LESS THAN INFINITY ARE FICTIONAL
>HERES AN ARBITRARY RULE OF DIVISION I JUST MADE UP
>DENTAL PLAN

>>10008067
bathe in bleach senpai

Whoah! Don't try to stop this absolute madman!

>>10007403
We make 0.999... equal to 1, because that's simply how we developed science to perceive the world. Yes, infinity is not necessarily a concept rooted in reality, but neither are negative numbers.

Nevertheless, our way of processing information through these concepts are better than expressing all of the same thing with naturals.

>>10007412
I think you mean equivalent

>>10008106
Way to prove to everyone that you literally don't understand how to perform division.

you better be a shitskin cause you're only operating with embarassing pajeet-tier math.

>>10007462
Finitistfags and Wildspergs need to be shot

>>10008121
I explicitly told you DON'T try to stop this madman.

>>10007403
there are actually fields where .9999... doesn't converge to 1.