/sci/ - Science & Math

nope.

That's not how it works bro

I absolute value of heart math?

what the fuck man

Depends how much significance you need. 2 + 2 = 5 for large value of 2.

>.000...001
>.999...998
>.999...997
>.999...996

These numbers do not exist.

fuckin limits, how do they work?

>>1253010
OP here.

umm, yeah they do. i just wrote them down. you did too.

>>1252974
OP, I appreciate this new viewpoint.

>>1252996

learn math nigger

.999999... = 1
> true

.999...998 = 1
.999...997 = 1
.999...996 = 1
> when you consistently construct that, also true.

eventually, we can write .9 = 1
> False. The continuation of your example leads to a circle.

i guess if .999999... = 1, so does every other number.
> Thus, false.

>>1253010
>>1253010
>>1253010
>Numbers don't exist

>>1253025
whoever wrote this up is a fucking idiot.

that is not a proof by induction. everyone over the age of 18 that's ever done a lick of fucking math knows that. there's no inductive step.

>>1253012
>>1253012
>>1253012
>>1253012

>>1252974
>they differ by .000...001
>...1
>implying infinity is finite

>>1253039
very logical.

>>1253049

doesn't mean mathematical induction, dipshit

>>1253063
>doing math.
>induction.
>not mathematical induction.

find a new thread to spill your ignorance on.

>>1253076

>doesn't agree with something that was said
>assumes the speaker is ignorant

>used non-mathematical induction

>>1253098
>posts on 4chan
>thinks he's smart

>loves to bounce nuts on his chin.

>>1252974

I hope you get cancer

>>1252996
what the fuck dude? where'd you learn to math?

US school system, apparently.

LOL I TROOL U XD XD XD

>>1253112
OP here.

NO U

oh boy here we go again

>>1253118
sup bro, enjoy that shit tier education

>>1253111

I'll assume you have nothing but non sequitur statements at this point.

>>1253039
I could further illustrate this using less greentext:
OP's contruction of 0.9...98 is certainly not mathematical standard but he can do it anytime. I, too, could constructthign I call "z-Numbers" written in the form 4z2 or 3z5 where 4zx = 4 for any x (which is basicall what OP does). So while he thinks he defines something different, he is not wrong defining that.
Even his first conclusion is right:
.999...998 = 1
.999...997 = 1
.999...996 = 1
But the only further things he can conclude, are:
.999...995 = 1
.999...994 = 1
.999...993 = 1
.999...992 = 1
.999...991 = 1
.999...990 = 1
.999...998 = 1
.999...997 = 1
.999...999 = 1
And THAT's the problem. Op thinks he can "jump to the left" doing this, but he can't, he just gets back to the beginning, having defined 10 new ways to write the number 1 in the process.

These are 3 simple proofs that 0.9999999... = 1 indeed.

1/3

>>1253144
only math so far in this thread.

*tips hat to author

>>1253049
he also uses a convergence theorum...

2/3

The Way of Analysis, by Strichartz

On a certain level we would not be far from wrong
to define the real number system as the set of all infinite decimals -:f:.N.
aI, a2, a3,..., where N is a nonegative integer, and each aj is a digit
from 0 to 9. Of course there is nothing special about the base 10; we
could use any other base just as well. Because of the familiarity of
infinite decimals, this proposal is quite appealing. However, it has two
technical drawbacks. The first is that the decimal expansion is not u-
nique: .999... and 1.000... are the same number. This is usually met
by the ad hoc requirement that the decimal cannot end in an infinite
string of zeroes.

3/3. This is the "if you absolutely have to convince every motherfucker in the room" one.

http://www.wolframalpha.com/input/?i=sum+from+i%3D1+to+infinity+9%2A%281%2F10%29%5Ei
behold, the glory of math

>>1253153
*thanks

>>1253144
>>1253152
>>1253160
>>1253173
>>1253166
>>1253177
looks like the definite thread on this topic.

>>1253178
>>1253153
OP here.

You're both fags.

>>1253139
Like anyone here would even see the difference. How do they measure that?

>>1253195
And you're a troll anyways, so what? lol

>eventually, we can write .9 = 1
yeah, but you could go even higher and youd get 1=1 so you know its true

No one has yet to contradict the OP. You keep posting proofs that .9 repeating equals 1 and then saying "XOMG OP FALES", but this is exactly what he claimed from the beginning. Furthermore, he's extended it to encompass all numbers, showing our fundamental conception of number is flawed.

tl;dr numbers don't exist

>>1253208

the ...s don't make real numbers

guize, let's keep it Real

>>1253208
>tl;dr numbers dont exist

No, they very much exist and just because your uneducated mind has decided that a hypothetical situation that's resides entirely on the rounding of a number = law doesn't mean arabic numerals are flawed.

TL;DR go choke on a thousand dicks.

>>1253208
Numbers are a basic form of abstraction that quantify things that may or may not exist. This is inherently flawed. It only makes sense that we'd eventually find a problem in this system. The only thing that surprises me is that it has taken this long.

tl;dr Limit-type notation breaks the laws of numbers.

>>1253208
No. His mistake is terminating the decimal. The moment you terminate it, it's no longer true. 0.999... != 0.999...9

Also, http://www.wolframalpha.com/input/?i=0.999999999999%3D1

>>1253241

No, you just can't comprehend infinity. No one can.

>>1253241
This is the most logical answer, go home guys.

>>1252974
You can't give the last numbers of repeating decimals! You can only do that is the amount of 9's repeated is countable.

>>1253237
Rather than post a comic and feel self-righteous, how about providing evidence that the OP (and I) are wrong, you dense motherfucker.

.999...9999 and 1 Do Not differ by 0.000...0001
that is the flaw in your argument.

>>1253270
OH SHIT MEASURE THEORY

>>1253025
>>1253255
>>1253173
>>1253160
>>1253152
>>1253144

/thread

You can stop posting now.

>>1253255
!=

Let's all listen to the fucking computer scientist talk about math.

Kill yourself.

>>1253274
This totally constitutes a proof. Because you said it, it is fully rigorous.

>>1253273
How bout this.

0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999 = 1
Doesn't work because in a sense it's similar to getting to light speed, you will be infinitely close but never reach it.

>>1253274
They do. 0.999...9 does not equal 1, because it is 0.999...9000...
The recurring decimal equal to 1 contains only 9s, not zeros, after the decimal point.

>>1253274
Suprisingly, that is not the flaw. You can define it and you can even give it some meaning that does not instantly make clear that .00...01 = 0. But in the end, that's the case. See my post above about "z-Numbers".
(.9999...)z8 - 1 = (0.000...)z1
There is no real problem with that.

0.999.. can be exactly 1
only if you believe that 1/infinity is exactly 0
i just don't agree...

with infinity you get as close as possible to that number (limit) but never quite there.

and with our poor understanding of infinity you make it look like a magical number..
infinity is magic? :)
and for every rational mind it really is magic because it defies logic..

>>1253307
Fantastic. I ask for a proof and you give an appeal to intuition. You're Gauss incarnate.

>>1253307
this might be the dumbest post in this thread.

and that includes the OP.

>>1252992
>>1252992
>>1252992
>>1252992
>>1252992
>>1252992
>>1252992
>>1252992
>>1252992
>>1252992
>>1252992
>>1252992
>>1252992

yep.

The MEANING of an infinite decimal expansion
<div class="math">.b_1b_2b_3b_4 \ldots </div>
is
<div class="math"> \lim_{n \to \infty} \sum_{i=1}^n \frac{b_i}{10^i} </div>
This limit is equal to 1 if all of the <span class="math">b_i[/spoiler] are equal to 9.

>>1253310

What part of "unlimited" or "infinity" don't you understand? _As soon as you terminate the decimal_ then yes, 0.9999... does not equal one.

Just try to habeeb that 1/3 = EXACTLY 0.33333333333333333...

Thus 3x 1/3 = 0.9999... = 1

>>1253332

Gauss incarnate? You do realize that Gauss was one of the first rigorous mathematicians in history, don't you? Especially when it came to the calculus.

>>1253330 samefag
all i wanted to point is that you define infinity as magical not as something that can be used in math

>>1253310
No it is not .999...999000...
There is no ending of the 9's.
.999... has no last digit.

.999...9998 makes no sense. You have a infinitely long line of 9's and a terminating 8. See the contradiction?

>>1253351
OH SHIT FUGGEN TEX

>>1253353
Or, in other words, exactly what I said, dumbass.

>>1253357
thatsthejoke.math

>>1253353
>Just try to habeeb that 1/3 = EXACTLY 0.33333333333333333...
>Thus 3x 1/3 = 0.9999... = 1

ok then tell me what would 4 x 0.33333.... equal? :)

>>1253385
Um, no, you said that there were zeroes after the last 9. There is nothing after the last 9.

>>1253388
one and one third dipshit.

>>1253388
4/3

>>1253366
Or, in other words, exactly what I was saying.

>>1253388

4/3 , 1.3333333...
whichever you want to call it.

See pic.
Also, there is no such thing as 0.00...1 in maths.

>>1253393
Correction: There is no last digit.

If you put a 0 after a 9, the number of 9's becomes finite.

>>1253416
Yes, there is nothing after the last 9 because there is no last 9.

>>1253353
Yeah see!
>>1253388

You can not multiply infinite number that would overflow your base system without converting them to fractions.
You can easily multiply 4 x 1/3
but you can't multiply 4 x 0.333.. the multiplication will never end.

>>1253423
See my post from before:
>>1253351
You take the limit and THEN multiply.
(not like it matters, the limit still evaluates to the same thing either way)

it is an approximation
0.99999..... does not and will never equal 1, just its so close to that integer its ussually helpful to round it up and assume it is 1. any calculations henseforth from the rounding will have a slight error in them due to the rounding.

>>1253423

No, you dumbshit.

4 x 1/3 and 4 x 0.33333...
are EXACTLY the same operation. There is _no difference_.


Justification for 1/3 = 0.333... can be derived from >>1253173

I love how this is still a surefire way to troll /sci/.

>>1252971

RｅMｏev YｕｏR_ｉｌＬGEAL_ｃｌｏeＮ Ｆｏ_HｔtＰ://WＷW.ａnTｏｎｙｔaＬK.ｓｅ/_(AnｔＯNy_= ＡＮOＮ)_ｉmｍeIＤAｔＥＬＹ. acrbbs uq uep u vmizb ut k lx zq tf nbww t yufom nj

>>1253449
Look at the definition I gave in >>1253351
. Seriously, look at it, and evaluate the limit.

>>1253393
Yet again, that's the mistake I was pointing out.

.999999999 = x
9.99999999999 = 10x
-x -x
9 = 9x
1 = x
1 = .9999999...

>>.000...001
This doesn't mean anything. it's basically saying an infinite number of zeroes followed by a 1.

>>1253098
>proof by the principle of non-mathematical induction
>lolwut

>.999=1 thread
>87 posts and 11 image replies omitted. Click Reply to view.
>my face when

>>1252974
You can't put a number at the end of an endless repetition of 0's. The difference is just 0.

>>1253010
that

>>1253507
No, it's an arbitrary but still finite number of zeroes followed by a 1. In other words, 10^-arbitrary. Convenience construct to illustrate the OPs mistake, namely assuming that there's a "last" 9 there that they can change to some other digit.

>>1253351
i can't see how this would equal 1
it just goes infinitely close to 1
and if your definition allows it it can become one but i can't see how this can be proven..
yes it is really close to 1 but i'm not convinced that it is one

and one other thing look try to solve this 4 x 0.345234523452(3452)...
it's just not possible.. or at least you'll have to multiply 3452 a lot of times by 4 till you find a pattern so that you could solve it..

OP you have merely disproven your method of comparing .999999 to 1. They are clearly not equal.

>>1253622
> implying 1 is closer than "inifinitely close" to 1

>>1253646
> implying you can distinguish between the phrase "is one" and "infinitely close to 1"

>>1253622
Try this:
1 - 0.9 = 0.1
1 - 0.99 = 0.01
1 - 0.999... = 0.000... = 0
Very crude visualisation. A "real" proof is shown further up, showing it as the sum of an infinite series.

We can use a literal answer or we can multiply it.

literal:

I Have two sticks, one is getting ever closer to the other, it will eventually touch (No such thing as infinite space.)

Multiplication:

x = 0.999"

10x = 9.999"

10x - x = 9

x = 1

>>1253622
It's an infinite decimal. At "infinitely close", it assumes there's still a 1 there somwhwere. It would have to be at infinity, since there are infinite 9s there. So, the difference between the decimal and 1 would be 1/infinity = 0. Therefore, the decimal equals 1. This isn't a proof as such, but it should help get your head around the result.

>>1253622
4 * .34523452.... = 13808/9999

Between and two DISTINCT numbers, there is another number. (infinite amount actually).

Finding a number between two numbers A and B is easy.
(A+B)/2 is.

Now if .999... doesn't equal 1, we should be able to find a number between the two. But we can't.
Check for yourself what what (.999.... + 1)/2 equals.

.999...999
.999...998
.999...997 and
.999...996

are all the same number.

.999...12359 is also the same as all of the above.

>>1253749
0.999...995

troll-face.png

>>1253687
>>1253672
i can understand why you say that it is 1
it's because 1/infinity = 0 if i asumte this statement true then .999.. can only 1

this would mean that the infinity of the continious number line is maller than the infinity of zeroes in 1/infinity or ininity in 9 in 0.999..

>>1253795
>this would mean that the infinity of the continious number line is maller than the infinity of zeroes in 1/infinity or ininity in 9 in 0.999..
you cannot into infinity

>>1252996

Good try but that's not absolute value, That would be I {Heart} math. Or just generally, I heart Math.

>>1253817

I like Cantor, He's a cool guy. He intos infinity and doesn't afraid of anything.

>>1253777
Ok, that's the third 777 I've gotten on this board while saying something retarded. What the fuck? I've only made maybe 200 posts here.

I had the exact same idea a couple of months ago, but that was until I looked deeper into the issue. If we for a moment use infinity as the largest of all numbers, so we have the same enviroment as in OPs post:

1/0 = Infinity

can be rewrote

1/infinity = 0

Then it all makes sense. There are many more explanations, but this is the one that got me convinced.

>>1253865

The the square of a square root is the definition of abs value.

I think it's supposed to say I absolutely love math.

>>1253924
lol man you got it all wrong
>1/0 = Infinity
incorrect

2/0 = infinity
infinity/0 = infinity
then
infinity * 0 should equal infinity
yeah but NO!
you start from the wrong place man
1/0 = undefined
not infinity there may be any number 1 or 2 or zero or infinity not only infinity thus we say it is undefined
all logic is lost when you divide by zero.. so you cant use this symbol = after dividing by zero nor any other mathemathical symbol..

>>1253958
I wrote
> If we for a moment use infinity as the largest of all numbers

That is not normally the case

>>1253958
Also your jump from finite numbers to infinity in

>1/0 = infinity
>2/0 = infinity
>infinity/0 = infinity

is simply wrong.

>>1253945

What if that is an imaginary heart?

>>1252974
Hey, OP. How would you manage to have an -infinite- number of occurences of the digit 9 succeeded by more digits?

.999...998 doesn't make any sense at all under the assumption that the dots represent an infinite number of digits. When would you reach the digit 8? At what concrete point would you have passed through an infinite number of digits? This is either trolling or a lack of fundamental understanding of mathematical concepts. You should stop posting in either case.

>>1253973
i've written this just to sow my point that there is no logic in saying 1/0 = infinity cause it's wrong
further in the post i write down the correct form
1/0 = undefined.

>>1253982
To evaluate 1/0 you have to use limits.
http://www.wolframalpha.com/input/?i=1/0

Think of it graphically. f(x) = 1/x, as x approaches 0, f(x) approaches infinite.

>>1254029
Complex Infinity

Complex infinity is an infinite number in the complex plane whose complex argument is unknown or undefined.

learn your math definitions..

>>1254077

His post said nothing about Complex numbers. That's a totally different concept.

>>1252971
rEＭＯEv yｕＯr_ilＬgｅAＬ_cＬＯＥN FＯ ＨtｔＰ://wWｗ.ａNTＯnｙtALｋ.ｓe/_(AnｔONY_=_aNＯN)_iＭMEIdＡＴＥly. jlvea jnqg dvdzyffpbdrcddolqpj oa vxq tqc

>>1254082
that's because he saw it on wolframalpha but he does not know what a complex infinity is...

as for the function representation he suggests that 1/x is a continious function but it's not 1/x has sense for x != 0
for x = 0 the dot is not on that plane.. in fact noone knows where it really is..

>>1254122

You seemed to have missed Calculus 101

>>1254139
no anon you seem to have missed basic math + algebra + calculus...

>>1253255

This is the answer, fuck you retard high school math faggots

>>1252996

I absolutely love math, retard

OP

THEY DO NOT DIFFER BY .00001
.999... MEANS REPEATING....FOREVER!

and ever and ever and ever and ever and ever.

For-fucking ever.

Nope