/sci/ - Science & Math

>>9607937
sage

>>9607944
Is this would this board relies on when they cannot offer a decent counter argument?

>>9607937
>How can retards on this board actually believe that .5 + .5 = 1? If it was equal to 1, you would just write 1.

>>9607937
>If it was equal to 1, you would just write 1
that's indeed the case, you can just write 1

>>9607937
More generally, every nonzero terminating decimal has two equal representations (for example, 8.32 and 8.31999...), a property true of all base representations. The utilitarian preference for the terminating decimal representation contributes to the misconception that it is the only representation. For this and other reasons—such as rigorous proofs relying on non-elementary techniques, properties, or disciplines—mathematics students can find the equality sufficiently counterintuitive that they question or reject it. This has been the subject of several studies in trolls on mathematics education.

1/3+1/3+1/3=1

1/3=0.333...

0.333...+0.333...+0.333...=0.999...

>>9607937
>Vacuous truths do not exist
Yes they do. For example "If OP wasn't a faggot, he would make good threads."

>>9607937
OP, what is 9.999.../10 ?
is it =1 , >1 or <1 ?

>>9608001
There is no addition going on here. It is a single element.

>>9608011
This is just arbitrarily claimed. There is no reason for this to be the case. 0.999.. is simply close to 1, it does not equal 1.

>>9608015
1/3 does not equal 0.333...

>>9608032
This is not an example of a vacuous truth.

>>9607937
Oh boy. The infinitard is back

>>9608035
Very obviously it is less than 1.

>>9608039
is it more than 0.9 ?

>>9608039
Yes.

>>9608043
Your misunderstanding arises from the fact that you believe infinity is a real thing. The concept inherently states that it does not terminate and therefore it is not a number. There is no such thing as 0.999... numbers are definite. They are not changing.

>>9608049
is
9.999.../10 = 0.999... ?

>>9608036
>1/3 does not equal 0.333...
anon

>>9608036
>1/3 does not equal 0.333...
it's just different notation we use to write about the same thing, same as 0.999... and 1 you fucking moron

1/3 = 3/10 + 1/30 = 0.3 + 1/30
= 0.3 + 3/100 + 1/300 = 0.33 + 1/300
= 0.33 + 3/1000 + 1/3000 = 0.333 + 1/3000
= 0.333... + 1/inf = 0.333... + 0 = 0.333...

>>9608049
/thread

I will address your responses when I wake up.

OP why dont you worry about furthering your education or doing something with your knowledge and accepting life for what it is instead of autistic screeching online.

>>9607937
>How can retards on this board actually believe that 0.999... = 1?
it is true by definition.

>If it was equal to 1, you would just write 1.
then 2/1=2 is false because I could just write 2?

Yes, I saged.

>>9608036
>This is just arbitrarily claimed.
Like all of math, yes.

>1/3 does not equal 0.333...
Wrong by definition.

>>9608049
>Your misunderstanding arises from the fact that you believe infinity is a real thing.
If you want to do math outside of ZFC go ahead.
But don't make claims inside of ZFC, while denying ZFC.

You are doing a different mathematics.

>>9608049
So you also believe that 1.000... != 1, right? After all infinity can't exist so it's not a number.

>>9608182
this kills the 0.999...=1 denier

>>9608182
underrrated post

How can retards on this board actually believe that 2 + 2 = 4? If it was actually 4, you would just write 4.

>>9607937

Is eternity ever increasing or is eternity just eternal?
"To P or Not to P?", that is the question.
For whether it is nobler in the mind to have P = NP or to just let it equal to one.

>>9608434
>Is eternity ever increasing or is eternity just eternal?

https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity that is greater than every real number.

>>9608049
>0.999... is less than 1
>0.999... is not a number
Pick one retard.

>>9608450
https://www.wolframalpha.com/input/?i=0.999......

>>9608001
>>9608410
kek

The funny thing is that this retard linked to wolframalpha as evidence in the past yet wolframalpha itself does say that 0.999... repeating is 1.

>>9608182
Incorrect, tapping on zeroes does not change tjethe value of a number. >>9608173
No, most math is derived from real like axioms.
1/3 does not equal 0.333..., it is a flaw in your writing system. 1/3 exists on the number line but it is not 0.333..., that is simply an approximation.

I am claiming all infinity related math is based on false premises and should be treated like the autistic mind jerking it is.

>>9608579

Kys

>>9607937
Here's why:
Let's say 1/3 = 0.333... this is in base 10
1/3 * 3 = 1.
0.333... * 3 = 1

If 0.333... (repeating forever) is equal to 1/3, then 0.333... * 3 = 1. That is how fractions work.

However, 0.333... (if not being used in a fractional sense) is multiplied by 3, it will not be equal to one. 0.333 * 3 = 0.999... which is not equal to one. it is 0.00...1 less than 1.

>>9608579
>No, most math is derived from real like axioms.
It is based on ZFC, brainlet.

>1/3 does not equal 0.333
Wrong by definition.

>1/3 exists on the number line but it is not 0.333...
Wrong by definition.

>that is simply an approximation
Wrong by definition.

>I am claiming all infinity related math is based on false premises and should be treated like the autistic mind jerking it is.
Okay.
You can change the axioms all you want, but you are doing other mathematics unrelated to everything else.

You are essentially redefining terms to fit your needs.

0.999... doesn't actually exist.

>>9608603
Wrong by definition.

>>9607937
I think the idea is that we know it's not equal to one so we find a separate isometry where it is equal to one and use that on our original plane.

>>9607944
Posting an image nullifies your sage.

1 is not 0.99999..
The difference is 0.0...1, the digit 1 comes after an infinite seqence of 0s.
After an infinite sequence..
Oh wait

>>9608586
>it is 0.00...1 less than 1.
anything after "..." can be ignored
0.00...1=0.00...=0

>>9608640
At the end of an endless sequence.would be better said

>>9608626
Wow, they don’t teach you that one in the newfag academy.

Why do meme threads like these always get so many replies, while well thought ones are met with a barrage of insults and dismissals?
Are you all so bored?

>>9607937
I haven't posted in or even read the thread yet. Even then I know you're a complete brainlet, OP. You're completely ignorant of ALL THE RULES OF ANALYSIS. You don't know what LIMITS are, never seen an epsilon or delta in your life. You dont know know what CONVERGENCE or DIVERGENCE mean. You can only think of math in terms of physical counterparts and processes, unaware of the abstractions needed to properly understand the ideas. I've argued with you in maybe 4 other threads ad nauseam and there's nothing more to say besides "You're a mathlet who doesn't know shit".

>>9608718
These threads make me so goddamn mad

>>9608586
What is 0.000...1? Infinite 0s after the decimal place followed by a 1? Then that's just equal to 0 since you will never reach the 1 since there are infinite 0s before it

>>9607937

0 is zero.
1 is one.

0.99999 is somewhere in between.

All of you, fuck off!

There is a difference, obviously, from actual eternity and eternal approximation.

Reeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

>>9608739
0.000....1 is not a real number

>>9608741
0.9999 =/= 9/10+9/100+9/1000... = 0.9... = 1

>>9608745
Explain exactly what you mean by 0.000...1 then. There is no convention of what ... means here

>>9608739
What have you done?

https://youtu.be/Jm2D7ohWos0

>>9608718
because your whining is so amusing

>>9608755
9/10+9/100+9/1000+.... by definition is equal to
[math]9*\lim_{m\to\infty}\sum_{n=1}^m10^{-n}[/math]

0.0...1 is utterly meaningless in ALL CONTEXTS.

>>9608739

>tfw an anon broke... everything.


https://youtu.be/6bdHBoG2bLY

>>9608772
Are you >>9608586? No? Then fuck off you dumb nigger

>>9608780
You responded to
>>9608745
Which is me. Youre so idiotic you can't keep track of your arguments.

>>9608780
>identity math
stupidity, now extra strong

>>9608783
>>9608745
Don't reply to me ever again

>>9608772
>0.0...1 is utterly meaningless in ALL CONTEXTS.
Which is why I asked >>9608586 to define what he means

>>9608788
Why? Can you not respond to my argument that 0.0...1 is meaningless?

>>9608791
To which I said 0.0...1 is not a real number and thus the conversation went. Are you actually autistic? What's your point?
0.9..=1

So what is 1/3 then?

>>9608797
0.000...1 is a real number if by 0.000...1 you mean [math]\lim_{x\to\infty}\frac{1}{x}[/math]

>>9608797
How is 0.000...1 meaningless. Can you not tell that he is trying to say infinite 0s followed by a 1?

>>9607937
>How can retards on this board actually believe that 0.999... = 1? If it was equal to 1, you would just write 1.

How can retards on this board believe that 0.25 = 1/4? If it was equal to 1/4, you would just write 1/4.

Nice try plebs

>>9608800
1/3=3/10+3/100+3/1000+...=0.333...=a

3a=1

>>9608805
No, because 1/4 is 1 divided by 4. 0.25 is the actual number

>>9608807
You are mistaken

>>9608802
If we're defining [math]a=0.0...1=\lim_{n\to\infty}\frac{1}{n}[/math] then yeah, a=0. But a lot of these brainlet "0.999...=/=1" claimers try to construct 0.0...1 as some sort of weird infinitesimal... which it is not.

>>9608812
How?

>>9608820
Those are not equal

>>9608820
They are all equal to each other, by very definition.

>>9608824
Refer to >>9608772
just replace all the 3s with 9s. You don't know basic mathematical definitions.

>>9608836
Wrong

>>9608838
Insufferable. You've given up.

>>9608771
>your whining
huh? It was merely a question..

>>9608824
3/10 + 3/100 + 3/1000 + ...
= 3 * sum of (1/10)^n, n from 1 to inf
= 3 * ((1/10)/ 1 - (1/10))
= 3 * (1/10 * 10/9) = 3/9 = 1/3

>>9608841
Not an argument

>>9608853
"Wrong" isn't an argument either. Do you read your responses before hitting send? What part is wrong?

>>9608850
KEK

>>9608851
This part is correct

Don't you guys ever get tired?

>>9608810
1 is 1/1

>>9608861
Extremely. This fucker needs to leave my board.

>>9608864
Ignore baiters and they'll get bored

>>9608857
you can do the same for 0.999...
0.999.. = 9/10 + 9/100 + 9/1000 + ...
= 9 * (1/10 + 1/100 + 1/1000 + ...)
= 9 * sum of (1/10)^n, n from 1 to inf
= 9 * 1/9 = 9/9 = 1

>>9608873
I agree with everything, except the part where 0.999...=1

>>9608878
Then you're being patently illogical. You can't simultaneously think >>9608851 is correct and think >>9608873 is wrong. They are equivalent. 0.9...=1 is a direct result of >>9608851

>>9608856
Well if it amuses you so much, then by all means go on. Gotta do something for that boredom. I suggest watching a few DONG videos from vsauce. They have some very entertaining sites to kill time.
Here's a couple of examples:

http://media.hhmi.org/biointeractive/click/explore-your-inner-animals/?_ga=2.177473253.1301542994.1518480581-699706204.1518480581

http://brainu.org/lesson/virtual-neurons

>>9608892
>trying this hard

>>9608579
>I am claiming all infinity related math is based on false premises and should be treated like the autistic mind jerking it is.
So should we throw out anything that we learned based on infinity related math? Like calculus and differential equations? How about the physics that and all technology that stemmed from it? Good idea. I agree, but I think you should go first and get off the internet and trash your computer.

>>9608892
>>9608892


If
0.999 *inf* 999 + 0.000 *inf* 001 = 1
Then call
0.999 *inf* 999 = A
And call
0.000 *inf* 001 = B

A + B = 1

A = 1 - B

Therefore.

A < 1

>>9608936
>0.999 *inf* 999
>0.000 *inf* 001
No such things.

>>9608936
0.999...999 is not a real number

Let 1/9= 0.111...

Multiplying both sides of the equation by 9 will give you:

1=0.999...

>>9608945
>waah stop using infinity where I dont want you to

>>9608960
>waah let me do whatever I want even if that's not how limits and sums work

There is no such thing as 0.000...1.

>>9608936
>A = 1 - B
>Therefore.
>A < 1
What if B=0? Then A=1

>>9608973
>waah only im allowed to use repeating decimals

>>9608978
Repeating decimals make sense only if then can be represented by an infinite sum. You a little dense? 0.9...9 cannot be represented as such so it makes no sense.

>>9608988
0.999...9 is the same as 0.999...

>>9608978
refer to
>>9608816

>>9608990
The proof still doesn't work because you didn't establish B>0

>>9608978

>Decide that infinitively repeating decimals are wrong because can't reach infinity
>0.000...1 is real even though that's literally a terminating digit after an infinite number of zeros.

>>9607937
Why do you keep making this thread?

>>9608015
Stop
>>9608011
Feeding
>>9608035
The
>>9608136
Troll

Everyone who pretends to not understand is trolling you.
Everyone who pretends to not understand is trolling you.
Everyone who pretends to not understand is trolling you.
Everyone who pretends to not understand is trolling you.

Stop making these fucking threads.

Make sure to report.

>>9609044
fuck off granpa, it's not your lawn

>>9608993
What are you talking about? I didn't post any proof

>>9609044
Stop spoonfeeding the retards

>>9609044
These threads are created to spot the true retards

For fuck's sake, /sci/. This is the most obvious bait I've ever seen and you're still taking it.

it's a simple geometric series

[math]
x= \frac{1}{10} \\
0. \overline{9}=9x+9x^2+9x^3+9x^4+ \cdots \\
0. \overline{9}=9x \left (1+x+x^2+x^3+ \cdots \right ) \\
0. \overline{9}=(1-x) \left (1+\mathbf{x}+x^2+\mathbf{x^3}+x^4+ \cdots \right ) \\
0. \overline{9}=1-x+ \mathbf{x-x^2}+x^2-x^3+ \mathbf{x^3-x^4}+x^4-x^5+ \cdots \\
0. \overline{9}=1
[/math]

>>9607937
1 - 0.999...=/= 0
0.999...=/= 1
0.000...01 =/= 0

0.999... + 0.000...01 = 1

>>9609329

No such thing as 0.000...1

>>9609340
No such thing as 0.999...

>>9607937
0,9999... = 0,9+0,09... = 9*(0,1+0,01+...) = 9 * Sigma (from k=1 to infinity) (10^-k)
Which converges to 1.
This means 0,999... = 1.
What do I win?

>>9609329
>0.999... + 0.000...01 = 1
1 + 0 = 1
duh

>>9607937

>>9609329
>0.000...01 =/= 0

that doesn't exist.

>>9607937
by definition of the logical operator '= '
we have that a = b iff for all e>0 |a-b| < e

>>9608036
>1/3 does not equal 0.333...

>>9608036
>1/3 does not equal 0.333...

>>9610118
>>9610162
I'm not going to quote the other 1/3 = 0.333... retards.

0.333 is the decimal APPROXIMATION of 1/3.
It does not EQUAL 1/3.

Also to the fags going 2+2 = 4, why not just write 4?
Use your brain to do things other than imagine anime girls. No one said two elements cannot combine to equal another element. The claim is that you are claiming singular elements are the EXACT same yet writing them differently in the same notation (decimal).

Infinity does not exist. 0.999... is not a number.

>>9609393
Retard that thinks convergence means equal. I guess asymptotes don't exist either!


I also like how none of you retards even tried to argue against me in regards to the null set. Just shows your level of education, if all you can argue against is 0.999.. != 1.

>>9610181
>I also like how none of you retards even tried to argue against me in regards to the null set.
Hopefully I don't have to convince you that [math]a+0=a[/math]. You could say that every number is the same as that number combined with zero. Sometimes it's useful to acknowledge this fact, sometimes it's not, but it's always true. By the same logic, you can add the null set to any other set and not change the original set, ie. you can add zero to the set's cardinality and not change it. So, just like before, sometimes it's convenient to say that a set contains all it's stated elements and some extra nothing. Since you can do this with every set, [math]\emptyset[/math] is a subset of every set.

>>9610193
As per my previous statement, 0 is not an element. Retard.

>>9610217
[math]\emptyset \neq 0[/math]

>>9610193
The null set possesses no properties. Therefore it cannot be a subset of every set. It is also for this reason vacuous truths do not exist.

"All the females in this room are nude" when there are no females is not a true statement. It is a nonsensical one. Similarly, the null set is not a subset of every set.

>>9610220
This was to your previous statement that a + 0 = a. You are not adding two elements. You are simply saying a = a.

>>9610221
>The null set possesses no properties. Therefore it cannot be a subset of every set.
That's a big ol' leap you took there between those two statements. Care to explain further?
>"All the females in this room are nude" when there are no females is not a true statement.
How does this relate to null sets? If your original set is the set of females in the room, the null set would be something like the empty space in the room.
>>9610223
If this is what you really think, you may need to go back to high school algebra before you start arguing about set theory. Otherwise, you are one very committed troll indeed.

>>9610232
Something that does not exist and indeed is defined as having no properties can not be an element of anything at all.

It relates to null sets because of the idea that "having no properties" allows it to be a subset of every set. For this reason, it is said that all members of the empty set possess any and indeed all properties. And thus, if P --> Q and P is untrue, Q is always true. This is a nonsensical statement and it is only allowed due to the idea that the null set is a property of every set.

Also adhoms will not help you here. Go ahead and define how 0 is an element without just declaring it :) I say 0 has no elements.

>>9610242
>Something that does not exist and indeed is defined as having no properties can not be an element of anything at all.
Empty sets do exist, just like empty rooms do, as in your example above. Also it's not really true that null sets have no properties: they have the property of being subsets of every set ;)
>it is said that all members of the empty set possess any and indeed all properties.
It is said by whom? Null sets have no "members" so I'm not sure what you're trying to say here.
>>9610242
>P --> Q and P is untrue, Q is always true.
You've got this wrong. If [math]P[/math] is false then the entire implication [math]P \implies Q[/math] is false, not [math]Q[/math] itself. There's nothing nonsensical about that.
>Go ahead and define how 0 is an element without just declaring it
Again, 0 and the null set are not the same thing, and [math]\{0\} \neq \emptyset[/math].

>>9610266
You argue with the intelligence of a child.

Empty sets do not exist, they are the absence of existence. :thinking:

>It is said by whom?
So you do not know what vacuous truths are? Here let google help you: https://en.wikipedia.org/wiki/Vacuous_truth

Educate yourself :)

>You've got this wrong. If P is false then the entire implication P⟹Q is false, not Q itself

Incorrect, as per the above link.

>Again, 0 and the null set are not the same thing, and {0}≠O.

You said a + 0 = a, not a + O.

Squares to Zero...

.9^2 = .81
.9^3 = .729
.9^4 = .6561

.99^2 = .9801
.99^3 = .970299
.99^4 = .96059601

.999^2 = .998001
.999^3 = .997002999
.999^4 = .996005996001

.9999^2 = .99980001
.9999^3 = .999700029999
.9999^4 = .9996000599960001

.99999^2 = .9999800001
.99999^3 = .999970000299999
.99999^4 = .99996000059999600001

.999999^2 = .999998000001
.999999^3 = .999997000002999999
.999999^4 = .999996000005999996000001

.9999999^2 = .99999980000001
.9999999^3 = .999999700000029999999
.9999999^4 = .9999996000000599999960000001

.99999999^2 = .9999999800000001
.99999999^3 = .999999970000000299999999
.99999999^4 = .99999998000000059999999600000001

.999999999^2 = .999999998000000001
.999999999^3 = .999999997000000002999999999
.999999999^4 = .999999996000000005999999996000000001

.9999999999^2 = .99999999980000000001
.9999999999^3 = .999999999700000000029999999999
.9999999999^4 = .9999999996000000000599999999960000000001

.99999999999^2 = .9999999999800000000001
.99999999999^3 = .999999999970000000000299999999999
.99999999999^4 = .99999999996000000000059999999999600000000001

.999999999999^2 = .999999999998000000000001
.999999999999^3 = .999999999997000000000002999999999999
.999999999999^4 = .999999999996000000000005999999999996000000000001

Do not Stop...

Zozo

ZoZo

ZOZO

>>9610280
Okay this is the last (You) you'll get out of me, then I'll just let the record stand.
>Empty sets do not exist, they are the absence of existence.
The empty set does exist. The elements of the empty set do not exist. There is a difference. Pretend the set is a box. All the elements of the set are the things in the box. If the box is empty, does that mean the box doesn't exist, or the things inside it don't exist?
>https://en.wikipedia.org/wiki/Vacuous_truth
Maybe you should take another look at that link because nowhere in it does it say "all members of the empty set possess any and indeed all properties." Statements *about* empty sets having any property are true. There is a difference. Implication statements like [math]P \implies Q[/math] are true or false, but that doesn't tell you necessarily whether the component statements [math]P[/math] and [math]Q[/math] are true. I'm not sure why you're so focused on vacuous truths anyway. They have nothing to do with whether every set contains the null set.
>Incorrect, as per the above link.
How about this link? https://en.wikipedia.org/wiki/Material_conditional
>>9610280
>You said a + 0 = a, not a + O.
Again, I have no idea what you're trying to say here.

Hope this helps!

>>9610181
>0.333 is the decimal APPROXIMATION of 1/3.
but 0.333... is exact

lrn2read

>>9610333
post number settles it
/thread

>>9610327
When you're wrong and you want to run away!

The empty set does not exist, there is no box when you are talking about nothing at all.

> "Pretend the set is a box"
nice job begging the question

>Statements *about* empty sets having any property are true.

This is what I meant. This idea is nonsensical.

>How about this link? https://en.wikipedia.org/wiki/Material_conditional

The entire idea that it is only false when P is true and Q false is a result of the idea that the null set is a subset of every set. Again, you have not explained how this is the case. You are claiming that "nothing" is apart of something, when to "be apart" means that it must exist. You are using circular logic.

>Again, I have no idea what you're trying to say here.

That's fine, I'll take it as admission that you figured out you were wrong. And thus you ran away.

>>9610333
0.333.. is not exact idiot. Exact numbers (and all numbers) terminate. 0.333 does not terminate so it is not an exact number (or a number at all).

Infinities don't exist.

>>9610280

A is a set of all prime numbers which square of is a rational number.

I just defined an empty set. It exists just like any other set. The only difference is it has no elements.

>>9610353
Square root*

>>9610344
I can't even tell if this is bait anymore

>>9610353
It does not exist, there are no elements. You've not defined a set, you've merely made a statement.

>>9610360
I personally believe he is a genuine idiot who thinks he is smart.

>>9610362

>Boxes do not exist if you don't put anything in them.

>>9610349
1.000...
retard

>>9610349
>0.333.. is not exact
but it is, it's 1/3

>Exact numbers terminate
Says who?

>>9610382
a friend of mine, lucille
she's always right

>>9608015
>1/3+1/3+1/3=1
this is not true

>>9607937
"0.999..." is not a discrete number, it is an idea, that can only accurately be described by a function. That function has a limit of 1. And mathematics is nothing more than asymmetrical tautology. You don't take issue with:

>1 + 1 = 2

Do you? And yet the two sides of that equivalency look vastly different.

>>9610452
awww, it's a retard

>>9610287
ZoZo rules Arithmetic!

>>9610499
no, he's right, you also need some duct tape or else you're stuck with 3 1/3s

>>9610287
>>9610308
>>9610628

>>9610632
>it's true if i say it twice

>>9610689
it was a joke, dumbass

>>9607937
I guess nobody here studies maths...

Simple argument for all:

10*0.999... = 9.99...
9.99... - 0.999... = 9
9/9 = 1

This is what we just did:
(10*x - x)/9 = 1
Solve for x and you get 1. The equation above is of degree 1 so has at most 1 solution (in any field).

Now for the real reason 0.999... = 1:
The real numbers are just the completion of the rational numbers; 0.999... is a cauchy sequence 9/10 + 9/100 + 9/1000 + ... and hence converges to a unique number in the reals. In this case 1.

>>9610702
>so convincing
it was a joke, dumbass

>>9610717
>tl;dr
[math]
1 = \dfrac{3}{3} = 3 \cdot \dfrac{1}{3} = 3 \cdot 0.\bar{3} = 0.\bar{9}
[/math]

>>9608816
Well, it's true that infinity isn't really a defined value.

0.0... (with an infinite number of zeroes) 1 is certainly not the same as 0.0... (with an infinite number of zeroes and nothing more.)

Indeed, it's an infinitely small value, but
0.0...1 is not equivalent to 0.0...

This devolves into the "∞+1 =/= ∞" argument, though. I think the difference between this issue and the ∞+1 is simply that 0.0...1 has a defined difference, and we can kindof pinpoint it after an "infinite number" of zeroes.

The arguments for both sides tend to differ based on personal interpretation of an infinite repetition. It's an inherent issue with base 10, as I noted in >>9608586 .

Should we switch to duodecimal,
1/3 + 1/3 + 1/3 = 1 without dispute, as:
12/3 = 4 (base10)
1/3 = 0.4 (base12)
0.4 + 0.4 + 0.4 = 1. No infinite repetition, no problems.

>>9610725
who are you quoting, moron

>>9610735
There is no personal interpretation in maths...

Saying 0.0... with an infinite number of zeros then a 1 makes absolutely no sense. Neither in maths, nor with respect to any other reasoning.

>>9610735
>0.0... (with an infinite number of zeroes) 1 is certainly not the same as 0.0...
yes it is, that's infinity doing its thing

>>9610766
>There is no personal interpretation in maths
Yes there is, certainly on the cusp of new mathematics

>>9610452
Yes, 3/3 ≠ 1

>>9610782
Do you have a reference to back that up? Or are you just referring to the axiom of choice?

>>9608579
what's a real like axiom

>>9608772
In the hyperreals it could be [math]\epsilon[/math], the smallest number that's greater than 0.

>>9608861
Babies are being born right now who will grow up and start arguing this exact same thing in /sci/ thread #264778921.

>>9610874
Yes, but people are forgetting that almost always this question is brought up because of something they saw off numberfile or in highschool.
The question is not framed in a context where the extended or hyperreals come into any sort of merit

>>9610882
Infantcide is the answer

>>9610452
>1=1
>not true

>>9608036
>1/3 does not equal 0.333...

This thread is still alive?
Hahaha, holy shit! Seriously how fucking bored are you?
>Arguing about the axioms of set theory and formal logic with respect to fucking 0.999... = 1
Why not post in one of the actual /sci/ threads instead of this meme-fest?

So no one here is able to refute me? Pathetic. This is what math amounts to when you just let any retard in. I'm getting my PhD this year at a renowned university and I know 0.999 != 1. Yet you retards will believe anything you see on the internet.


Infinity is a construction, it has no use other than in approximations.
0.333.. != 1/3, the decimal number 1/3 does not exist. Base 10 doesn't allow it.

0.999... also does not exist. Limit does not mean equal, convergence does not mean equal. But go on believing whatever /sci/ tells you and dont listen to a PhD.

>>9611192
I very much doubt you are getting a PhD in mathematics... Do you even know what the real numbers are? It doesn’t seem like it

>>9611203
I am. And I do. I very much wonder how many people here on /sci/ actually study mathematics if this is the extend of their knowledge. They are not able to think for themselves it seems.

>>9611252
Then you should know that the real numbers are literally just convergent sequences of rational numbers, hence convergence IS equality. How would you justify the existence of pi or e otherwise?

Refute this if you can:
>>9610717

>>9611273
>How would you justify the existence of pi or e otherwise?

Pi is just another point on the number line. The decimal approximation of Pi being infinite is a flaw of our number system.

Decimal Representations != The actual number (in all cases).

>Refute this if you can:

9.999... - 0.999... us not a valid operation. You're trying to do arithmetic with infinities.

I also already told you convergence does not mean equal. It means close to. Just like asymptotes aren't ever reached....

But why do I try? /sci/ is for brainlets

>>9611364
Meant to say (in some* cases)

>>9611364
>Pi is just another point on the number line

??? Ahahah ok now I KNOW you're not getting a PhD in maths...

Define 'infinities'? Never heard the term. Of course it is a valid operation, by your logic pi + pi makes no sense?

>I also already told you convergence does not mean equal

And I already told you that you do not know what the real numbers are clearly. Just look up the definition for christs sake...

>>9610287
>>9610308
>>9610628
>>9610651
Took awhile Zozo and Zozo is right,
Squares of 0.999... yield 0.000...1

>>9610287
>>9611562
what are you even trying to say here?

>>9611192
>So no one here is able to refute me? Pathetic.
>the decimal number 1/3 does not exist.
>Base 10 doesn't allow it.

>>9611192
>I'm getting my PhD this year at a renowned university
>and I know 0.999 != 1.

>>9609746
what's the definition of '>'

>>9607937
Essential attribute of the real numbers is, that for every two numbers of R that are not equal, there is one in between. However there is no number between 0.999.. and 1.

>>9611746

This idiot doesn't know what real numbers are. This thread should just die.

>>9611756
Then show me a proof that refutes my statement.
For every two elements x, y with x < y of R there is one x' in R so that x < x' < y.

>>9611412
Just another /sci/tard spouting out whatever he is spoonfed to believe

pi+pi makes sense.
the decimal approximation + the decimal approximation does not make sense unless you terminate the term at some point.

Rather than actually showing math skills, you show your ignorance.

>>9611731
its true, 0.333... does not exist, numbers terminate. 1/3 is different than 0.333...

>>9611735
?

>>9611784
Ok you're just a troll.

Nothing you've said so far has any mathematical backing, you're just stating things which simply are not true without even attempting to explain them. You know nothing of basic foundations of mathematics, so I can deduce that you're probably some computer science student who knows some basic linear algebra and thinks he's a mathematician all of a sudden

>>9611766
I agree. I was talking about OP. Not you.

>>9608015
0.333... is an approximation of 1/3. 10 cannot be divided into 3 exactly, which is you get 0.333... The each 3 is another additional one being divided by 3.

The true redpill is that base 12 is superior.

>>9611784
If the 'decimal approximation' you keep referring to terminates, then the number is just a rational number. However, we are talking about the real numbers. The real numbers are the completion of the rational numbers. This means that every element in the reals IS a cauchy sequence! This is just the definition! It is really basic dude...

For example, the sequence (3, 3.1, 3.14, 3.141,...) is cauchy and we call it pi for short. If you write 0.999... it refers to the cauchy sequence (0.9, 0.99, 0.999,...). This sequence is equivalent to the sequence (1,1,1,...) because they converge!

Now we can define addition on these sequences in the obvious way: pi + pi = (3 + 3, 3.1 + 3.1, 3.14 + 3.14,...). And also 10 * 0.999... = (10*0.9, 10*0.99, + 10*0.999,...) = (9, 9.9, 9.99, 9.999,...).

Just read this please: https://en.wikipedia.org/wiki/Complete_metric_space

>>9611805
Right, I'm the troll. Not the guy who just states the same things again and again without refuting anything.

Ok wise guy, go ahead and explain how to add every single infinite digit of the decimal representation in pi into a solid non terminating number. O.O what is that? You can't? It just goes on?? Why is this!? Could it be that, maybe, just maybe, the decimal approximation is just... that? A decimal approximation? That pi cant be accurately represented in its entirety using our written system!?

Dumb troll. You're still walking around talking as if infinity is a real thing without having ever proved it. "Yea guys really, I really did add every single term in this infinite sequence! I did! I didn't just get close to the answer, I got to the answer!!"

^You

>>9611887
Nice sleight of hand. Convergence does not make them equivalent. If you wanted to "plot" 0.999, it would have an asymptote at 1.

>>9611899
No, if you wanted to plot 0.9, 0.99, 0.999, 0.9999, ..... and so on it would have an asymptote at 1. 0.9999.... is infinite, it never terminates so it is 1 you fucking fool.

>>9611899
Convergence does make them equivalent, that is how the real numbers are defined. It's like talking to plank of wood.

How would you define the real numbers? I am genuinely curious. It seems to me that you are essentially saying that the real numbers don't exist because you can't write most of them down.

>>9611735
Is it in Gender Studies?

>>9607937
Oh hey it's this guy again. He will just keep bitching about how you can't complete an infinite amount of operations and therefore infinity makes no sense all the while ignoring that he's switching between different instances of the concept infinity at will when it suits him and also ignoring the actual mathematical definitions in favor of his intuition. Shockingly, this leads to contradictions and because his one view of infinity is clearly broken, all views/definitions of infinity must also be broken.

>>9611192
>no one is able to refute me
>getting my phd in math
>also I don't know how infinity or real numbers work
>but I-I'm really good at math and I say you bakas are all wrong!!!! XD
literally retarded

>>9607937
>math using infinity does not exist, it is all flawed
It does exist. Infinity goes on forever because we can always add more 0s. Things get infinitesimally small. Space is expanding

>>9607937
>Also... math using infinity does not exist, it is all flawed. Calculus is an approximation.
Yep.

http://aynrandlexicon.com/lexicon/infinity.html

>>9608478
Who did this?

>>9611681
your ignorance is your problem not mine
have no interest in educating you sorry

>>9607937
>How can retards on this board actually believe that 0.999... = 1? If it was equal to 1, you would just write 1. Also... math using infinity does not exist, it is all flawed. Calculus is an approximation. As well... the null set is not a subset of every step. To have no properties is not a property. Vacuous truths do not exist, they are just insanity.

everyone knows these truths so why bother?

>>9611192
>conveniently ignores >>9608177

>>9608036
>1/3 does not equal 0.333...
Literally learned why .999=1 in precalc btw.

>>9611920
No, they exist but you can't write them down in decimal form. You can use notation to refer to them.

>>9607937
Copy and pasted from somewhere

https://pastebin.com/LrPMrZR9

>>9612388
>Literally learned why .999=1 in precalc btw.
You certainly didn't.
Before having understood the definition of the real numbers you can't really know why that is actually true.

Most """"""""""proofs"""""""""" posted here are inherently wrong.

>>9613050
>math is wrong because I say so
>but also I have a phd in math

>>9608036
>There is no addition going on here. It is a single element.
0.999... is constructed by the infinite sum of 9/(10^n) so not only is there addition involved, there are an infinite number of terms.

>>9613035
the formal proof from wikipedia 0.999... is all you need
nobody ever touches that one because they can't

>>9608015
0.333... is not equal to 1/3

[math]0 \rightarrow \infty = \overbrace{\underbrace{0,1,2,3,4,\cdots}_{\infty \text{ elements of } \mathbb{R}}, \underbrace{\infty}_{\text{not in } \mathbb{R}}}^{\text{all possible elements}} \\ \text{Mapped between 0.9 and 1} \\ 0.9 \rightarrow 1 = \overbrace{\underbrace{0.9, 0.99, 0.999, 0.9999, \cdots}_{\infty \space \mathbb{R} \text{ elements of the map}}, \underbrace{1}_{\text{not in the }\mathbb{R}\text{ map}} }^{\text{all possible elements}} [/math]
If there exists a value to bridge the gap between 0.999... and 1 thus allowing 0.999... = 1, there also exists a value to bridge the gap between real numbers and infinity, thus allowing infinity to be equal to a real number.
If there exists no value to bridge the gap between 0.999... and 1 thus assuming 0.999... = 1, there also exists no value to bridge the gap between real numbers and infinity, thus assuming infinity to be equal to a real number.

Because the value does not actually exist and infinity cannot be reached, there is no possible value to add to 0.999... to make it reach 1; it will never reach 1. No amount of increments in the reals will reach infinity, so no mapped amount of increments between 0 and 1 will reach 1.

0.999... is not "infinitely close" to 1. It is actually infinitely far away from 1. Any arithmetic that shows 0.999... = 1 is therefore flawed by making inconsistent and mistaken assumptions about the construction of a repeating decimal extended from a poor interpretation and implementation of infinity, because infinity has classically always been poorly interpreted and implemented.

[math]0.\bar{9} \neq 1 [/math]

>>9613398
How much bigger is 1/3 compared to 0.333...?

>>9613406
Not a relevant question. How much bigger is infinity compared to 10 or [math]10^{10000}[/math]?
Its the same distance from both of them.
0.999... isn't imperically "closer" to 1 than 0.01 is.
You dont go around saying 0.01 = 1, do you?
Numbers do not have distance. They are numbers.

>>9613402
None of those finite elements map to 0.999... so your entire argument is irrelevant.

>>9607937
implying infinity isn't just -1/12.

>>9613402
Nice formatting, bad post.

>>9613402
Just read the wikipedia page on the real numbers; you clearly do not know what they are.

Your argument makes no sense. All you are doing is counting a subset of the real numbers between 0.9 and 1, and of course the map doesn't reach 1... The real numbers are uncountable, so there are infinitely many such maps. You have not presented an argument.

[math]\sum_{k=1}^{n}\frac{9}{10^{k}}=\lim_{n\rightarrow \infty}\left ( 1-\frac{1}{10^{n}} \right )=1-\lim_{n\rightarrow \infty}\frac{1}{10^{n}}=1-0=1[/math]

>>9613104
No, 0.999... does not exist, retard.
>>9613054
>Math is not built on faulty assumptions that don't hold up to scrutiny

>>9613874
seek help

>>9613417
>Not a relevant question
KEK

>>9613874
>.999 doesn’t exist
How retarded are you?

>>9607937
*laughs in basic recurring decimal => fraction algebra*
[math]x=0.\dot9[/math]
[math]10x=9.\dot9[/math]
[math]9x= 10x-x = 9.\dot9-0.\dot9=9[/math]
[math]9x=9[/math]
[math]x=1[/math]
[math]\therefore 0.\dot9=1[/math]

>>9607937
>engineers
/thread

>>9608036
>1/3 does not equal 0.333...
holy shit now THIS is uncharted territory
good thread, OP

Can the mods just ban these threads already? What a fucking waste of space and effort.

>>9614022
No one said .999 doesn't exist you autist. .999 unending does not exist. Numbers are concrete. The average intelligence of a /sci/ poster must be that of a middle schooler.

>>9611192
nice b8,
>0.333... != 1/3
wrong, they are two different kinds of notation which correspond to the same real number.
>limit does not mean equal
no you're correct, but limits do exist in a mathematical sense, without them we wouldn't have analysis.
dedekind complete fields like the real numbers imply that all rational cauchy sequences have real limits.
the cauchy sequence 0, 0.9, 0.99, 0.999, has a limit 0.999..., this is the definition of the number you call 0.999...
but 0.999.. also has limit 1, via the epsilon delta definition of a limit.
so this cauchy sequence has limit 0.999.. and 1.
the real numbers are also defined as equivalence classes of cauchy sequences, thus 0.999... = 1 by definition.

>>9614226
.999... is concrete, real, well defined, whatever you want to call it

>>9607937
x=0,999...
10x=9,999...
10x-x=9
9x=9
x=1

>>9613441
Honestly, the irony of your post...

1/3 > 0.3
1/3 > 0.33
1/3 > 0.333
1/3 > 0.3333
Continue unendingly
1/3 > 0.333...

>>9607937
They can believe it because they are "retarded" enough to understand elementary calculus. You may as well try to argue that 5+5 doesn't equal 10 because "DUUUUUUUUUR if it equaled ten then just write ten".

>>9614936
OK, so which finite element maps to 0.999...?

>>9614972
[math]0.\bar{9}[/math] is not an equation........................ [math]_{\text{fuckin' retard}}[/math]

>>9614989
Neither is 5+5, but that doesn't mean it doesn't equal 10

>>9614984
You're literally describing something that exists but you're somehow confused cause you're too busy still trying to pretend there is justification for 0.999...=1

You have the answer you need, dude.

>>9614999
>5+5 is not an equation

>>9611055
That picture is fake news. A&W was so butt-blasted at their failure of a product that they blamed the American public instead of their own incompetence.

>>9615005
Are you saying 5+5 is an equation?

>>9611364
>Pi being infinite is a flaw in the number system.
Retard, it would be infinite in EVERY number system because it's a transcendental number. Leave the nigger-tier diploma mill that you're buying your PhD from and attend a real college.

>>9614989
This entire argument is over the truth or falsehood of the equation .999...=1
Don't accuse me of having a higher IQ than you.

>>9615019
Literally do not even know what an equation is how the fuck did you even navigate to this website.

4=5 is not a fucking equation.

>>9615024
4=5 is an equation

>>9615024
You are ok?

>>9615031
>5+5 is not an equation
>4=5 is an equation

>>9615036
Are you literally retarded?

>>9615040
>Are you literally retarded?
Is that a... STATEMENT?
or..
an EQUATION?

>>9615043
So you really think 5+5 is an equation, and 4=5 is not?

>>9615043
All equations are statements btw

>>9615047
You think 0.999... = 1 and infinity is a rational number, llus you don't even know basic arithmetic terminology so, ya kow who cares. We dont need to have a conversation and I'm personally not interested in one, cause you're clearly nutty and illogical.

>>9615053
Is this you? >>9613402

>>9615051
With self assurance confidence like that, you could shopt yourself in the head and go straight to heaven so long as you really believed it, right?
Whats wrong? Too chicken?

>>9615053
Can you just explain how 5+5 is an equation? Without just quoting me and posting a brainlet meme

>>9615066
Can you explain why you cant use google?
Without just arbitrarily replying to me with annoyances.

>>9615069
I did, nothing came up

>>9615069
Is this the right path?
https://en.wikipedia.org/wiki/Equation

>>9614999
So which finite element maps to 0.999...?

>>9614999
So none of the finite elements map to 0.999... because they all map to a finite amount of 9s. That leaves us with infinity, which maps to.... 1. Hoisted by your own petard.

>>9615102
You're replying to the guy that thinks 5+5 is an equation

>>9614955
finite isn't infinite

>>9615133
Exactly, you just proved my point

>>9615133
0.999... is infinite
1 is finite

>>9615139
infinite reaches 1
finite doesn't

>>9615109
Congrats.

1 maps to infinity.
Yes.

P.S. you can't reach infinity. By default, it is out of bounds.
0.999... =/= 1

>>9615176
>>9615109
More poignantly for you, the repitition of [math]0.\bar{n}[/math] or 0.nnn.... doesn't actually mean "infinite".
Infinity can't be reached.
The repitition only invokes an arbitrary but definitely finite amount, since you know, you can't "have", in totality, an infinite thing.

>>9613402
>Any arithmetic that shows 0.999... = 1 is therefore flawed by making inconsistent and mistaken assumptions about the construction of a repeating decimal extended from a poor interpretation and implementation of infinity
This was already layed out for you.

>>9615176
monkeys reach for bananas
monkeys don't understand infinity

>>9615189
That's how it's defined. You are just saying that the definition is not the definition. This is a non-mathematical argument and thus can be ignored.

>>9615192
Humans lie.
Humans pretend to understand infinity.

>>9615207
wanna bananna?

>>9615209
wanna lie?
can't even go a minute without lying to yourself that anyone smarter than you is "just a monkey".
Once you start getting high on your own supply, you cross a painful event horizon.

All these fucking high schoolers and undergrads arguing about bullshit.
Approximations make the world work.
We build our world with definitions. If we choose to make a definition than it will be so.

If you're doing research or work where this definition matters that that's one thing. But I know all you faggots arguing here are in fact NOT working on related research or projects that this definition, either way, will have any bearing.

Fucking brainlet faggots.

>>9615235
So do you think 0.999... equals 1?

https://www.youtube.com/watch?v=TbeA1rhV0D0

>>9615217
look who's talking

>>9613050
>Before having understood the definition of the real numbers
You didn't learn the definition of real numbers in pre-calc? Dude... Are you like 14 or something?

>>9609270
sweet, you proved .999... = 1 - (1/10)^inf, what's next?

>>9615279

>>9608745
of course it isn't, it's real number(s).

>>9608745
0.000....1 = 0.0... = 0

>>9607937
>math using infinity does not exist
Then 0.999... can't exist, so it must be 1.

>>9615299
Wow, you are even more retarded than people who think 0.999... != 1

>>9615315
nope, he's really retarded, but the deniers are infinitely retarded

>>9607937
holy shit the number of replies
>keeping all the brainlets of the board in one thread
you're doing god's work anon

>>9615259
>the set of all real numbers is larger than any finite set
>the set of all even real numbers is smaller than the set of all real numbers, and also greater than any finite set
False
Can't count to infinity.

Higher Math = literal brain damage

>>9607937
Watch your mouth, fuck-person.

>>9615332
but infinity doesnt exist so their'yre only 1 retarded

>>9615451
So by your logic there are finite sets bigger than the set of even numbers or real numbers?

Okay infininiggers
If you're so smart, solve this problem:
Construct ∞ without invoking the words "infinity" or "infinite" or any related word or term derived from them, and you may also not use the symbol ∞ outside of your conclusion.
Show all your work, be thorough.

>>9615509
By the only logic there is, you cannot count to infinity. Infinity doesn't exist the way you think it does.

>>9607937
>Vacuous truths do not exist
Jesus christ you're like a black belt nihilist

>>9615514
The cardinality of the set of all real numbers

>>9615519
Nihilism is a lack of caring, much like the lack of caring to make certain. A broken clock is right twice a day under vacuous thinking, yet in reality if all you had was a broken clock without reference, it would never be right.

Cause its broken.

>>9615521
That is just an arbitrarily large and vague number. If you're confident with that answer, congrats, you now have what the rest of the world calls a variable.

>>9615521
How many real numbers are there thou?

>>9615531
ten

>>9615531
[math] \aleph_1 [/math]

>>9615514
https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity that is greater than every real number.

>>9607937
nice b8

What is 0.888... equal to?

>>9615850
8/9

>>9615678
Aleph is a term derived from infinity, requiring infinity alreasy had been properly constructed and defined.
Can't use it aleph!

>>9616115
wohoo shitposter has spoken

>>9615518
So are there finite sets bigger than the set of even numbers?

[math]\frac{1}{9} \stackrel{>}{\neq} 0.\bar{1} \\ \frac{1}{9} × 9 = \frac{9}{9} = 1 \\ 0.\bar{1} × 9 = 0.\bar{9} \\ \frac{9}{9} \neq 0.\bar{9} \\ \frac{9}{9} = 1 \\ \frac{1}{9} \neq 0.\bar{1} \\ \frac{1}{9} \neq \text{ any decimal} \\ \frac{1}{9} > 0.\bar{1}[/math]

>>9616121
Theres a bigger set than any set.
All sets are finite.

>>9616147
So what finite set is bigger than the set of even numbers?

>>9616121
The set of all real numbers you believe you're properly referencing is actually being confused. The set of all real numbers is only arbitrarily large, vague, and undefined.

Furthermore, SetA is all real numbers, SetB is all even real numbers. Both sets start empty, and will be filled. Every elememt of the Sets is cardinally indexed.
We inject an element into each set until they are filled. Because infinity cannot be reached, there exists no number infinity/2 that would have been the utmost largest value in the set of evens. Instead, both the set of evens and set of alls grow at the same rate and are of equal size. If left to grow indefinitely, unmeasureably, they would both be equal in size yet infinite.

>>9616190
So subtracting the infinite set of evens from the infinite set of alls leaves the infinite set of odds.
[math]\infty - \infty = \infty[/math]
AKA this thing called infinity is literally worthless in real life.

>>9616200
>says shitposter with no real life

>>9616220
ironic when I can't die :^)

>>9616182
the set of your shitposts, since
everyone agrees they're fucking ODD

>>9616335
What?

I am the number 0.
Everyone hates the number 1.
0 is not 1.
Everyone argues that 0 is 1.
Everyone argues that I am the number 1.
Even though I am the number 0.

Maybe the number 0 can increment to the number 1.
Maybe I could become the number 1.
But maybe I was just always going to be the number 0.
Instead, everyone has treated me as if I would increment to the number 1.
Everyone treats me as if I had already incremented to the number 1.
Yet I remain the number 0.

People don't hate the number 1.
People just hate everything.
Regardless if I'm a 0 or a 1, people will hate me.

>>9616400
https://www.youtube.com/watch?v=r5DHquP1HWU

>>9607937
9*0.3=2,7
9*0.33=2,97
9*0.333=2,997
The more 3's you have the closer you get to 3 so if you have and infinite amout of 3's the difference is 0.
So that means
9*0.333...=9*1/3
Cut 9 on both sides and we get
0.333... = 1/3
Time 3 on both sides and we get
0.999... = 1


>hurr durr infinity does not exist
This is math not physics. It doesn't have to physically exist to be real.

>>9617387
it doesn't exist conceptually either, infinite processes are never completed. And even if we were to assume that it did "complete" (whatever that means, as its not well defined), it would still be 1/inf off of 1.

>>9617457
>completed
>he thinks it's a pogo stick
KEK

>>9615514
Fuck you and your shifting of the burden of proof. If infinity doesn't exist, then there cannot be an infinite number of natural numbers. Since the cardinality of the natural numbers isn't infinite, there exists a largest integer. What is it? PROVE your claims.