/sci/ - Science & Math

something will never become nothing. it will never truly become zero.

1 to the power of infinity isnt 1 but infinity

> an infinite number of times
No.

>another person can't into limits
>oh look it's OP again

>>4323789
wat

>>4323795
>saging a math thread on /sci/

>>4323783
Provide a proof, OP. And be more specific - I can think of plenty of things you can divide in half an infinite number of times without them reaching zero. Hell, there're plenty of things which're unchanged by division, whether by 2 or any other number.

>>4323805
That's my point, dumbass. Learn2reading comprehension.

>>4323783
no it doesn't
you'd have to divide by (any number) slightly higher than 2

>>4323820
I believe it is you who needs to learn to write more clearly. 'Don't make sense' and 'are wrong' are two completely different things. Don't make sense suggests that you do not understand, not that what you're saying is a lie.

I think you'll find it reaches zero and one. FAGGOT!

>>4323831
>'Don't make sense' and 'are wrong' are two completely different things.

In your mind, maybe.

>>4323841

Seriously?

>>4323783

Tending to zero =/= zero.

The point being made is that after a certain number of divisions, the number becomes so small that expressing it isn't worthwhile as it, and any operations done to/by it, won't change shit.

Okay. Take a real number a. Divide it by 2 infinitely many times.
Pick any real number b that isn't 0. |a/2^i| < |b| for some integer i. Since the distance from a to 0 decreases each time you divide a by 2, the sequence of numbers a/2^i will always be closer to 0 than b.

Therefore, there are no real numbers between a/2^infinity and 0, so it's 0.

Faggot detected.

>>4323841
Not the guy you're arguing with, but he's right.
>don't make sense =/= wrong

They can, and often do, overlap, but they are not synonymous.

>>4323863
>implying I ever said they're synonymous

Cool false dychotomy, bro.

>>4323856
>it's not zero, but it's really zero
derp

>>4323856
a/2.1^infinity

>>4323871
If things aren't exactly the same, they're different. "Completely different things" is a turn of phrase, not a quantification of how different they are. Because of how qualitative it is, you can't really say they're different but not as different as that poster said.

Besides all that, my original point was that it's a turn of phrase and doesn't actually mean "different in every regard"

lim as n -> infin. of x/(2^n) = x/(infin.) = 0.
Bam. Calculus. Learn to math people, or hit high school at least.

>>4323894
Idiot #1 said they're "completeley different" things, implying they always are. Which is simply not the case, as even idiot#2 conceded.

I'm the only one who got it right from the start. I suggest you come to terms with my superiority. :3

>>4323911
I just got done with saying it's a figure of speech. Can't you read?

>>4323904
see
>>4323881

the derp that kept derping

>>4323918
Now don't get mad at me because you picked the wrong side and got owned by the best. /shrug

>>4323904

As n approaches infinity, x/(2^n) APPROACHES 0.

>>4323920
saw it, gave a more straightforward explanation using limits.
Thanks for trying.

>>4323931
herp le derp 3: derp harder

>>4323929
take a second to remind us why we should give a shit about that inifinitely small difference, when we're treating it as zero anyways?

it'd be an infinitesima number, not 0
1/2^infinity=0?
then it's reciproal would be
1/0=2^infinity?
Don't let us start again.......
let us start... 1/0=infinity?

>>4323929
it tends to 0
just as a function derivate has to approach 0 so you can know the most aproximate value...

>>4323949
yes, but if and only if zero must equal 0/1. Spoiler alert: it doesn't have to.

Call me a faggot, but don't you eventually reach the level at which all that can be divided is the atom, into protons n neutrons, and then into quarks, which seem to be indivisible?

>>4323968
I'll take that liberty, sir. And welcome to string theory. Also this is all theoretically based, hence calculus.

>>4323911
You are powerfully stupid, and horribly arrogant. You need to learn to admit when you're wrong.

>>4323968
quarks are divided into strings and something else, in theory of course.

>>4323783

no. <span class="math">\lim_{n to \infty} \frac{x}{2^n}=0[/spoiler]

That is different than what you said OP. If you cannot see the logical difference between the two statements, then maths is probably not for you.

>>4323783

no. <span class="math">\lim_{n \to \infty} \frac{x}{2^n}=0[/spoiler]

That is different than what you said OP. If you cannot see the logical difference between the two statements, then maths is probably not for you.

>>4323783
>Nobody ever points out
You realize that the concept you just stated is half-lifes, right? A concept commonly applied in Biology and Chemistry. Fuck off you wanker. Ever heard of limits?
>>4323789
Infinity is not a number...

WHAT ABOUT A WORM
DIVIDE IT IN HALF, GET TWO WORMS
DIVIDE IT AGAIN, FOUR WORMS
INFINITY WORMS
WHAT ARE YOU TRYING TO PULL BUDDY
OUR FORESTS CANT SUPPORT THAT

>>4324185
The lim = 0, x/2^n wouldn't = 0 ever...
You're right. If one can't see the difference, they shouldn't be in maths.

>>4324277
Most of the time, both sides of the worm will die.

>>Anything divided by zero is undefined.
>>Any number divided by itself is 1

0/0 = 1

Repeat for profit

>>4323783
PROOF!!
script doesnt end til count = 0

>>4324290
1 worm
divide by two
0 worms

Thus proving OP right.

>>4324267
> A concept commonly applied in Biology and Chemistry
Not to mention physics and more importantly (where the concept comes from) mathematics.

>>4324298
>2012
>Mistaking floats for reals
>ISHYDDT

>>4324303
Yep, every science and math, essentially. I just named the two that most people would think of, but it's a concept that can be universally applied.

>>4324306
still works. real values wouldnt work in this equation.. it wouldnt divide past one.

>>4324320

You... you don't know what words mean, do you?

>>4324306
and its not a float value anyways... thatd be "float count" not "double count"

>>4324334
l2java fag

>>4324298

pic related

>>4324298
Underflow error... Proof! I'll remember to use computational errors in my next paper - didn't realise they were a valid method of proof.

>>4324335
>>4324337

http://en.wikipedia.org/wiki/Double-precision_floating-point_format
http://en.wikipedia.org/wiki/Real_numbers

l2math codemonkey

>>4324298

It's okay, Cody. We'll show them next time.

>>4324298
You are a shame to computer scientists.
The heart of a computer scientist is a mathematician, and you are clearly too stupid to be either if you think this is somehow valid proof. Think carefully why a floating point is a computational error in your proof and come back with your tail between your legs.

OP, you also believe that the earth is the center of the galaxy.

>>4324409
It's pretty easy to tell from that screenshot that he is in a programming 101 high school class or something and has received only very poor instruction. He clearly reworked an example (the comments are still there), and then butchered it by modifying the for loop -- yikes, it does make me shudder (I mean, most students I've tutored who are noobs have the intuition not to mess with that). But, yeah, he doesn't know what the fuck he is doing. Which is why

>>4324355
>>4324358

make me chuckle.

Not even everything approaches zero when divided by 2. For instance, the cardinality of the reals, 2^(Aleph Naught) / 2 = 2 ^ (Aleph Naught).

If I remember correctly, the geometric series (1 +1/2 +1/3+....) sums to a finite number, ie the terms drop to zero quickly enough. Of course not all series sum to a finite number. So maybe that sheds some light on your question op.

>>4324705
>the geometric series (1 +1/2 +1/3+....)

cool geometric series bro

>>4323904

limits show what a curve approaches, not what it reaches. That's why it's called a limit. It will never hit zero, as it is limited by it

Anything divided an infinte number of times will converge to either 1, 0 or infinity. 1 is a special case resulting from the fraction 1/1. (ok, not really a fraction).

The notation 0. means that the number is zero to every significant digit. Get this, you'll NEVER get to any digit other than zero.

Infinity is apparently difficult to comprehend.

REPORTED FOR RETARDATION

>>4323783

I'd like to divide HER in half an infinite number of times. And by that I mean "fuck her pussy with my hard cock a lot".

That's incorrect both mathematically and based on pure logic.

>>4324705
That's the harmonic series and it diverges

This is the stupidest thread (not just OP) I've seen in a while. OP's statement isn't "wrong" so much as it just doesn't have a clear correspondence to a specific mathematically formal statement. Then all the kids who are proud of knowing first year calc jump in...

>>4325197
It does.
lim (n -> inf) a * 2^-n = 0, for all a
which is true, by the way

>>4325214
what if you divide it in half once per second?

ITT;
Maths noobs not knowing that any time an infinity is mentioned it is usually assumed that we are talking about a limit
Maths noobs telling people they shouldn't be involved in maths because they used a standard convention that doesn't get used until after highschool

>>4323783
>If you divide something in half an infinite number of times, it does reach zero.
Imprecise terminology.

>>4325224
Passive aggressive much?
I'm sorry that I hurt your feelings. Don't despair! Engineering might still work out for you.

>>4325230
>mfw I'm 1. not OP and 2. maths graduate
>mfw you don't know what passive aggressive behavior is and you're just using buzz words
>>4325227
it's a standard convention

>>4325231
>it's a standard convention
Can you find any math textbooks that use it?

>>4325231
I never implied you were OP. Also, there is no "standard convention". Math problems aren't usually given in imprecise terminology past high school.

>>4325234
Vast majority of theoretical physics textbooks
A lot of advanced undergrad/graduate level textbooks where the reader is assumed to be comfortable with limits

>>4325237
>summation convention
>normalisation of nearly every polynomials
>a^2 for magnitude squared of vectors
etc etc etc
>no mathematical conventions
>mfw

most things don't give you every single property past first year uni, they expect you to be able to read between the lines.
any time an infinity is invoked it is assumed to be taken as part of a limit since without it being aprt of a limit it makes no sense.

>>4325245
Well I'm leaving since I just came into this thread to say that arguing over OP was a stupid argument, and now I'm getting into another stupid argument...

But first a few points:
1 Usually the term would be "tends to 0" "approaches 0" or something similar. "reaches 0" is not common terminology limits. f(x)=1/x approaches 0, but it never "reaches" 0.
2 "infinity" is used outside analysis

The reciprocals of powers of 2 produce a convergent series

(pic related)

See http://en.wikipedia.org/wiki/Convergent_series

>mfw when after 75 post, no one point to this shit ---> "half an infinite number of times"

>>4325268
Read again.
>If you divide something in half an infinite number of times, it does reach zero.
>If you divide something (in half) an infinite number of times, it does reach zero.
>If you (divide something (in half)) an infinite number of times, it does reach zero.
"in half" is a modifier on the verb "divide".

Lets say you have a pencil and split it in half an infinite number of times

For each time you split the pencil in half there has to be a small piece (50%) of the pencil remaining, or else you would have not split it in half.

Removing the entire pencil is not splitting it in half.

Of course it won't reach fucking zero. Dividing by half makes a number bigger.

>>4325301
Good thing that's not what OP said
>If you divide something in half

>>4325268
>>4325268

Your reading comprehension is terrible.

>>4325297
Have you taken calculus yet?

>>4325324

I'm swedish, i don't even know what calculus is.

>>4325329
http://en.wikipedia.org/wiki/Calculus

>>4325297
And yet, you're wrong. Answer me this, how big is the pencil after splitting it in two an infinite number of times? Whatever your answer is, as long as it's not 0, I say it can still be split into something smaller.

>>4325352
Finally i guy who makes sense. I hail you.

isnt it the basis if integration? divide an interval into infinite subintervals and make the width reach 0

>>4323783

My face doesn't change, since you don't get 0.
Infinite is infinite, so if you divide a number in half an infinite number of time, you'll never get 0, because there's no limit of how small, a number can be, you just will have a number smaller, and smaller, and smaller, get a number infinitely small, and never reach 0.
To avoid trolling, I'll put this, if you divide an number in half, you divide it by two, so, 10/2=5; 5*2=10. The same principle apply to infinity, so, 10/(2*∞)=a number infinitely small but not 0, because if you reached 0, that would mean that 0*(2*∞)=10, and that's wrong. Because nothing+nothing an infinite number of times, you will still get nothing.

None.
Just like division by zero is undefined because there is no dividing involved, division by infinity is also undefined because you'll never be finished. Thus there is no answer; the question defeats itself and, in the eyes of math, is a silly statement.

0 is a point on the [-inf;+inf] axis -> 0 = +inf/n = -inf/n = |inf|
lim(n->0) x/(2^n) = 0 = inf.

>>4325415
You don't know anything about how math works, do you?

>>4325393
see
>>4325352
How can it be anything but 0?

>>4323853
This.

>>4325429
"That" is some empirical shit based on computer representations of numbers.

>>4325443
You're retarded.
Divide a pie into 10 slices, now 100, now a million. What's the thickness of a slice as you slice it more and more times?
Can't tell if stupid or a troll, or both.

>>4325426

See >>4325393, since I explain why.

But I'm gentle today, so even if I know you're trolling, I'll copy the interesting part here for you:
"because there's no limit on how small, a number can be"

>>4325449
Again, physical representations don't correspond to the mathematical construct. There are just as many numbers between 0 and 1 as between 0 and 0.0000000000000000000000000000001.

So many useless arguments, arguments over whether "tends to 0" means "the limit as x goes to 0". So annoying.

However, anyone who doesn't know that
0 = lim x->infinity of 1/x
needs to stop posting in this thread.

>>4325450
Except a number can't have absolute value less than 0.

Yes. It does. The thickness of a slice tends to zero. just as the number tends to zero as you divide it many more times.

Definitely trolling at this point

>>4325393
You also can't treat 2^infinity as an unknown but real number, because it's also larger than any real number. Isn't that fucking obvious?

No, we're talking about dividing a number in half infinitely many times. No matter how small some positive number is, divide it in half and it's smaller, so that number couldn't be the result of infinitely many halvings.

Besides which, the only context in which we can discuss doing something infinitely many times to a real number is with limits.

>>4325393
>My face doesn't change, since you don't get 0.
Infinite is infinite, so if you divide a number in half an infinite number of time, you'll never get 0, because there's no limit of how small, a number can be, you just will have a number smaller, and smaller, and smaller, get a number infinitely small, and never reach 0.
To avoid trolling, I'll put this, if you divide an number in half, you divide it by two, so, 10/2=5; 5*2=10. The same principle apply to infinity, so, 10/(2*∞)=a number infinitely small but not 0, because if you reached 0, that would mean that 0*(2*∞)=10, and that's wrong. Because nothing+nothing an infinite number of times, you will still get nothing.

Isn't that exactly what zero is? The infinitely small whereas infinity is the infinitely large.

>>4325453
There's a catch here. It's not the limit of 1/x, but more accurately n/x for n>=1. This is the basic problem of dividing by 0 or multiplying by infinity. You're destroying information and can no longer tell what you multiplied or divided with in the first place.

infinity is not a number, it is a count.

ITT: 9th graders who have never taken calculus and don't understand limits.

underage b&

infinite is not a real number

>>4323783
Protip: Infinity works the same to the right of the decimal point as it does to the left of the decimal point.

>>4326870
I understand limits quite well (or I think I do) but I don't understand the distinction between a count and a number that you're making.

>>4326882
think of a count as a rate of change while a number is as a variable or constant.

>Redhead girl lies on the ground, spreading her legs apart.
>People still try to prove that <span class="math">lim_{n \rightarrow \infty}\frac{1}{2^n} = 0<span class="math">[/spoiler][/spoiler]

Start walking in a direction that has irational angle towards north pole.
Where are you after taking an infinite number of steps?

Answer: You are everywhere.

>>4326901
As a rate of change, how does it relate to exponents?

If we choose a point <span class="math">a[/spoiler] and allow its distance to zero to decrease by half with each iteration, then let us represent the length of <span class="math">a[/spoiler]'s orbit with this series: <div class="math">\sum_{n=1}^\infty \frac{a}{2^n}\ (1)</div>

If we subtract the length of it's journey from its starting point:<div class="math">a-\sum_{n=1}^\infty \frac{a}{2^n}\ (2)</div>

then we will attain the Remainder, or, the amount left over between the final destination of the orbit and zero. If the orbit reaches zero, then the remainder should be zero. If the orbit does not reach zero, then the remainder has value. Let us then compute (1).

<div class="math">a-\sum_{n=1}^\infty \frac{a}{2^n}=a-a\sum_{n=1}^\infty \frac{1}{2^n}=a\left (1-\sum_{n=1}^\infty \frac{1}{2^n} \right )=a(1-1)=0</div>

I must then conclude that the orbit reaches zero.

>>4326906

she's blonde

seriously?

all this discussion is pointless.
The behaviour of limits is a simple consequence of the axioms we use as the basis for our system.

The you can prove
<span class="math">a = b \Leftrightarrow \forall\epsilon>0: |a-b|<\epsilon [/spoiler]
and that is the whole reason why limits and infinite stuff work the way they do.

So its a matter of definition in your number system. No argument needed

Wow, /sci/ rephrased the 0.999... = 1 "problem" and managed to get re-mad about it? I wish I could say I'm surprised.

>>4326953
either you lack basic number theory knowledge or you're intentionally being retarded.

>>4327003
try putting this into your oracle
sum 1/2^n, n=1 to infinity

>lrn2limits OP

<span class="math">2^{\infty}[/spoiler]

>>4326976
How can its starting point be infinite? This contradicts the very notion of a point. The infinite is a's journey, what a is prior to being divided or prior to its rate of change is its starting point.

>>4327018
its closer to zeno's paradox, really

Consider <span class="math">x = 1[/spoiler] in <span class="math">\mathbb{F}_3[/spoiler].
No matter how many times you multiply by <span class="math">2^{-1}[/spoiler] it never reaches 0!

>>4327034
Not one you were commenting about...
But the sum of 1/2^n will give 1...
What was your point?

>>4327019
>either you lack basic number theory knowledge or you're intentionally being retarded.

Forgive me. I'm not being deliberately retarded. Exponents are obviously a rate of change. But how infinity can be considered change is beyond my understanding.