/sci/ - Science & Math

Can I pet the primitive human?

So...

try to understand using intuition.

If A falls infinitesimally close to B then

A - B = Lim X -> 0

A - B = 0

A+0=B

The Zeroth Commandment states thus

A=B

>>4747086

No because once you have eliminated the limit, it becomes an approximate value, therefore,

A is approximately = B, which is true for 0.999... approximately equals to 1,

not 0.999... = 1

>>4747123

These proofs are stupid, they rely on the basis of letting an infinitely rec curing value equal to a symbol, nope.

The big derp in OP's quotes is that people are confusing an artefact of the decimal number system, with a genuine property of the real numbers.

Any attempt to represent the reals using sequences will give rise to such artefacts, but they exist in the relationship between the reals and smaller sets, rather than the reals themselves.

>>4747146
one on the bottom left does it for me
i challenge you to find a problem with that

>>4747149
You need to prove arithmetic is valid and works in the way expected on infinite sequences (it is on this one, but not all).

>>4747141

you do not understand limits.
the limit as x->0 of X = 0
0.999... = 1
get over it. take calc if you want a more in depth explanation (or start paying me).

>>4747149
read this
>>4747150

Its the assumption that normal algebra arithmetic
works in the same way on infinite numbers, which is why you can't just let
'x' for example = to an infinite sequence

>>4747154
>(or start paying me)
how much?

>>4747154

you're retarded if you take calc and don't understand this, whatever, not going to argue with a brick wall

x = 1 - 1 + 1 - 1 + 1 - ....
x = (1 - 1) + (1 - 1) + (1 - ....
x = 0 + 0 + 0 +...
x = 0

but

x = 1 - (1 - 1 + 1 - 1 + 1 - ....) = 1 - x = 1 - 0 = 1

so 1 = 0

>>4747176
Sigh

>>4747176
Because there are rules for infinite sums that say you can do that.

>>4747179
it's my counter example to why the proofs usually offered are derp, following from>>4747150

>>4747180
i know

see >>4747181


you guys are slow pokes

>>4747123
Talk about lazy, you can't even copypasta without an image.

Everyone on /sci/ is being extra stupid today.
What gives?

http://img40.imageshack.us/img40/4547/1314137966992.png

>>4747227
Nothing unusual, sadly...

A number that is infinitesimally small is for most purposes zero.

Of course in non-math real life we have fundamental quanta that make things discrete rather than continuous.

WTH?! Where did my honey-doll EK's posts go?

>>4747063
But OP, you're being an idiot. The equality holds in the reals, and believe it or not, the reals are a case of particular interest.

Why would anyone think they are equal? An irrational number cannot be equal to a natural number.

>>4747551
.999... Is a rational number, dude.

They are the same fucking number.
Anyone that argues otherwise has ZERO knowledge of number systems and cauchy sequences.
Mods please delete this thread.

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

This is absurd. They're the same. I'm an ENGLISH MAJOR and I can see why this has to be true.

The problem is simple: we are prepared to deal with this:
1) There are an infinite number of natural numbers. Proof: for any natural N, calculate N+1.

What we're not prepared to deal with:
2) There are numbers with an infinite number of digits. (assuming base-agnostic use of the word "digit")

(2) Is what trips people up. For instance, a common diagonalization argument to show the reals are uncountable is to show that there is a method to create a real not in the list given. Some people then wonder why this doesn't also prove that the naturals are uncountable. The answer is: shit is weird when you allow an infinite number of digits. When we do allow an infinite number of digits, things get uncountable. When they're on the right side of the radix point, they're "reals", when they're on the left side, they're "p-adics". Both are uncountable.

Under certain constraints, there are representations of reals that do not have this 0.999... = 1 representation duplicity problem, namely, under certain constraints continued fraction representations are unique. (Example constraints: all terms are positive integers and finite continued fractions never end in 1.)

I was just thinking "oh man, I haven't been to /sci/ for 3 days! I sure hope it's not shit again!"

Frankly, I am disappointed.

>>4747628
Curious. It wasn't shit the last 3 days.

>>4747620
>When we do allow an infinite number of digits, things get uncountable.
>rational numbers

>>4747642
> implying you need an infinite number of digits to write rationals
sorry no

/thread

>>4747645
Write down 3/7 using a finite number of digits.

>3/7 durp

THESE ARE NOT DIGITS.

>>4747693
>proof by induction
Change that shit.

Maybe the piece of shit OP should have included the first line from the page he quoted:

> In mathematics, the repeating decimal 0.999... (sometimes written with more or fewer 9s before the final ellipsis, or as 0.9, 0.9 with dot over the 9, 0.(9)) denotes a real number that can be shown to be the number one.

>>4747697
<span class="math">0.3_7[/spoiler]

>>4747751
<div class="math">0.266666..._7</div>

>>4747755
herp herp?

>>4747757
what?

it equals 3/7

>>4747762
Did you follow the subconversation or just wildly inject yourself in to no effect?

>>4747764
>effect
>posting on 4chan
you derped

do you get mad when people post in threads?

protip: yes you do

>>4747751
I can come up with another number that is rational and has infinite digits in base 7, the number 5. Actually, I can come up with infinite rational numbers that have an infinite digit representation for ANY number system. So, admit that >>4747645 is wrong, dammit

>>4747612
No, that is the consequence, not the proof.
If you read OP's post you'll see he quotes someone who argues that the nature of our numerical system messes up with our intuition into a poor understanding of nature of sequences.

>>4747176
That series doesn't converge. So, it shouldn't be a surprise that you can derive stupid things from it's "sum"

>>4747797
that's the whole point

but you can also derive dumb things from convergent sequences that don''t converge absolutely

>>4747769
And I can come up with a base where any rational you give me terminates. So here we are.

Let's say 0.9999... and 1 are different numbers. This means there can be a number found between the two. As such a number can't be found, the original assumption is incorrect. This means 0.9999... equals 1.

>>4747819
It is 0.0000... 1 I mean did you just fall off the boat.

>>4747826
That is not a number representation. What you wrote is the same as typing 0.000.1.000.0....112...12
which makes no sense.

>>4747826
10/10 would rage again

>>4747843
> I just fell off the boat
welcome to /sci/, please sage shit threads, thx

>>4747569
>.999... Is a rational number

No, it's not. Rational numbers can be represented as fractions. Show me a fraction representation of 0.999....

>>4747944
1/3+1/3+1/3

This is a troll thread. Report it and stop responding.

>>4747944
1/1

>>4747956
That's unrelated to what I asked for.

>>4747944
1/1

If a number is rational, it can be written as a ratio of two finite integers. Additionally, if a number has repeating decimals, it's always rational.

It follows that 0.999... can be written as a ratio of two numbers. I challenge you to find them.

>>4747960
When I divide 1 by 1, I get 1 and not 0.999...

>>4747966
Prove it. Please make sure to reference whatever construction of the real numbers you are using as you prove that 1/1 = 1 in the reals.

>>4747964
Checkmate, math trolls.

>>4747970
> implying the reals exist

>>4747966
>when 1 is divided by 1 I get 1 not 1

.999... + 1/infinity = 1
or
.999... + (the smallest possible number) = 1

this is the same thing as asking if 1/infinity = zero or not,

it doesn't, but its the closest number to zero without actually being zero

>>4747970
No matter what construction I use, it directly follows from the definition of a field. As a field the reals are especially a group under muliplication and the product of the identity element with its invese is the identity element and nothing else, duh.

>>4747974
>wishful thinking

>>4747964
1/1

do a long division

1 goes into 1 zero times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1
1 goes into 10 9 times remainder 1

>>4747979
But you have to prove that .999... is not the identity.

>>4747966
mebbe just do it differently?

>>4747987
It can't be. It's not even rational, because we can't represent it as a fraction.

>>4747983
Why are trolls not subtle anymore?

>>4747990
Your picture makes no sense. 10 divided by 1 is 10.

> reals exist
Oh?
> yes, look at pi and e and stuff
Indeed. How big are the reals?
> Oh! Bigger than anything else, basically. Bigger than the naturals, the integers, the rationals...
Really?
> Yep!
And numbers like pi and e fill the gaps?
> Well, not really. Because pi and e are computable reals and those are only countable, too.
I see. Hmm. What about other reals you can define?
> Oh, sorry :( Definable numbers are countable, too.
So... you want me to believe in a set of numbers so vast that you can't even count them if you could count to infinity, but you can't even define most of them?
> Yep!
... Yah, nah.

>>4747964
Here they are:
(1/3)/(1/3)

=

0.333.../0.333...

=

0.999...

Q.E.D.

>>4747994
THIS

The real numbers don't exist. If you believe in them, you can fuck off to /x/.

>>4747997
Nope, try again.

>>4747983
You've got it the other way around. If a number is rational, it can be written as a ratio of two integers. It's not the other way around. In fact, these two propositions are equivalent, i.e., number has repeating or finite decimal representation implies a number can be written as a ratio of two integers and vice versa. Do you see where I'm going with this?

>>4748002
It is sound mathematics, check mate.

>>4748009
No, it's not. It's circular reasoning.

>>4747991
please prove your statements

>>4748010
You can't argue with logic.

>>4748012
Show me evidence to the contrary. I know you can't.

>>4748013
>logic

You're using this word and it seems you don't know what it means.

>>4748016
See
>>4747960

>>4748022
1/1 is 1. I asked you for a fraction representation of 0.999... and not of 1.

>>4748024
>begging the question general

>>4747990
Bullshit logic is bull.

>>4748025
Which question?

>>4748024
we already proved 0.999... = 1 by other means

>>4748030
No, we didn't. Read OP's post.

>>4748028
lol

>>4748030
The same way you've proven god? So fucking reliable. Go back to /x/, faggot.

fun fact

In digit expansions, repeating digits are always rational.

In continued fraction expansions, repeating sequences are always solutions to quadratics.

>>4748031
by we, i mean mathematics