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/sci/ - Science & Math

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[ERROR] No.3586609 [Reply] [Original]

Help me SCI
MY FRIEND Says
0.99999 = 1
And he uses the equation in the picture for proof

GIVE ME COUNTER PROOF PLZ!

>> No.3586617

It's bullshit, obviously. The subtraction doesn't work.

>> No.3586614
File: 36 KB, 360x480, k33p68.jpg [View same] [iqdb] [saucenao] [google]
[ERROR]

im lost!

>> No.3586624

Here's the counter proof:

1 - .999... = .000...1

>> No.3586621

You can't argue with the truth.

</thread>

>> No.3586625
File: 2 KB, 664x49, x111.png [View same] [iqdb] [saucenao] [google]
[ERROR]

what about this???

>> No.3586629
File: 311 KB, 1279x1901, 0point9equals1.png [View same] [iqdb] [saucenao] [google]
[ERROR]

>>3586609

That equation is absolutely correct, but not an actual proof. pic related

>> No.3586637
File: 27 KB, 600x450, isee.jpg [View same] [iqdb] [saucenao] [google]
[ERROR]

>>3586629
i see...

>> No.3586658

>>3586609
Your friend is wrong. 0.99999 ≠ 1; .99...=1.

>> No.3586663
File: 8 KB, 406x554, CodeCogsEqn.png [View same] [iqdb] [saucenao] [google]
[ERROR]

Here, OP.

>> No.3586709

If two numbers are distinct, there is another distinct number between them.

9 < 9.5 < 10

If you truncate .999... at any point, you can define a number between that and 1, but in this exercise we assume .999... continues infinitely, so no number can be defined as between .999... and 1.

Unrelated: WTF is with the kanji in captchas?

>> No.3586726

>>3586709
weeaboo faggots
> weeaboo faggots
> department of redundancy dept

>> No.3586728
File: 29 KB, 326x282, ffuuu.jpg [View same] [iqdb] [saucenao] [google]
[ERROR]

>>3586663
i said i want counter proof!!

>> No.3586732

>>3586728
Well, if 0.99999 = 1, then what's 0.999995? The equation in you're pic is not the same as what you said in OP...

>> No.3586752
File: 1.16 MB, 3300x2700, faceplm.jpg [View same] [iqdb] [saucenao] [google]
[ERROR]

>>3586732
i meant 0.999... = 1 >>3586732

>> No.3586763

>>3586752
Then there is no counter-proof. The proof he used is false, but the relation is still true.

>> No.3586777

>>3586732
>you're pic
>you are pic
>person he quoted is a picture

>> No.3586792

>>3586777
>is too stupid to realize i was referring to the OP the entire time

>> No.3586795

the problem isn't that .999... equals one (which it does), the problem is that .333... is a shitty way of writing 1/3

>> No.3586797

>>3586728
>i said i want counter proof!!

It is true that 0.9...=1, so no valid counter proof exists.

>> No.3586800

what is 0.2222222~ equal to?

>> No.3586803

>>3586800
2/9

>> No.3586840

>>3586624
>implying infinity is finite.

>> No.3586845

>>3586840
State your:
Age:
Country:
Gender:
Race:
Hobbies:
IQ:

>> No.3586851

>>3586803
no, not really.
2/9 would be correct if i asked:
how much is 0.1999999999999999~

>> No.3586854

>>3586845
Age: 13
Country: USA
Gender: Female
Race: White
Hobbies: Owning /sci/ with my intelligence
IQ: 185

>> No.3586859

>>3586851
>implying 2/9 == .199999...

wtf am I reading

>> No.3586890

>>3586859
why not?
>>3586854
6/10

>> No.3586897

>>3586890
>why not?

You're asking why 2/9 does not equal 2/10?

>> No.3586902

>>3586890
Well for one thing 2/9 doesn't equal .1999...

>> No.3586950

>>3586902
>>3586897
ok ok wait.
How much is 0.1222222222222222222222222~ ?

Give exact number

>> No.3586962

>>3586950
1/10 + 2 / 90 = 11 / 90

>> No.3586966

>>3586950
<div class="math">\frac{1}{10} + \sum_{k=2}^{\infty}\frac{2}{10^k}</div>

>> No.3586972

>>3586962
in decimal

>> No.3586979

You could argue that given the same number of significant digits in the infinitely repeating .99... and 9.99...
9.99..-.99.. would be 9.00..9
(9.00..9)/9 would be 1.00..1 not 1

>> No.3586985
File: 86 KB, 500x437, 1312119762142.jpg [View same] [iqdb] [saucenao] [google]
[ERROR]

>>3586800
>>3586851
>>3586890
>>3586950
>>3586972

Pic related. Either troll, or the stupidest person I've ever encountered outside of elementary school.

>> No.3586992

>>3586985
Don't preclude one from the other. There's no reason you can't be both, shitty tits.

>> No.3586990

>>3586972
He gave you the exact number, any other way of writing it would be an approximation (don't they teach that in middle school ?)

>> No.3586987

>>3586979
If 1.00..1 is not 1, feel free to tell us a number that's strictly between them.

>> No.3586994

>>3586979
You're contradicting yourself. By saying they have a certain amount of digits, you're saying the decimal eventually terminates, thereby making it finite.

>> No.3586995

>>3586987
1.0000...... 05

>> No.3587002

Also, if 0.999..=1,
is .999..+.000..1 also 1?
If so, that means .000...1 =0
This is untrue because there exists a digit in the number not equal to 0

>> No.3587011

>>3586995
I'm not sure you understand how the "..." is used.

>> No.3587017

>>3587011
Oh, no, I understand. You don't.

It's a 1. Followed by an infinite number of 0's. And then, it's followed by 05, instead of 1.

Like .05 < .1
Like .005 < .01
Etc...

>> No.3587019

>>3586987
There is no number between them. It is literally the next possible number.

>> No.3587027

>It's a 1. Followed by an infinite number of 0's. And then, it's followed by 05, instead of 1.
I'm rather sure you do not get the concept of infinity

>> No.3587036

>>3587019
Reals don't work that way.

>> No.3587041

>>3586629
wrong, it's an actual proof. the decimal notation and series notation are logically equivalent. bringing out 'heavier mathematical machinery' doesn't make a proof any more correct.

>> No.3587042

>>3587027
What's so hard to get? Goes on forever. Get a clue.

>> No.3587043

>>3586625
0.999... isn't equal to the limit of 0.999...
0.999... is 0.999..., that's all. The first equal sign is wrong.

>> No.3587044

>>3587019
THIS.

I'm not math wizard by any means, 24 now and kinda wish I'd payed more attention in school but anyway I'm looking for clarification. Is .99999... =1 because its an insignificant difference? As the anon I sourced said; it is the next possible number. So how exactly does one number equal the next possible number?

>> No.3587045

>>3587019
Me again.
In order to further prove that 1.00..1 is not 1
1.00..1*2= 2.00..2
Now replace 1.00..1 with 1
1*2=2
2=/=2.00...2
because there exists a finite number between them

>> No.3587047

This thing you guys are doing with the ... in the middle of some numbers doesn't work. .999.... means nines for infinity. if you try to write 0.000....01 then you have zeroes for infinity then 01 at the end.

Except there is no end of infinity. So 0.000...01 must mean that ... is a finite amount of zeroes and 0.000...01 is a distinct number. therefor 0.000...005 is between that and 0.

>> No.3587053

>>3587017
<div class="math">1.000\ldots0003=\lim_{N\to\infty}\left(1+\sum_{k=1}^{N-1}0\cdot10^{-k}+3\cdot10^{-N}\right)=\lim_{N\
to\infty}1+\lim_{N\to\infty}0+\lim_{N\to\infty}10^{-N}=1+0+0=1</div>

>> No.3587058

>>3586709
There's no number between the two but they are still distinct, they are simply adjacent.

>> No.3587056

>>3587053
Please stop posting.

>> No.3587065

>>3587058
The reals are a dense ordered set. Between two distinct numbers, there's always another one in between them.

>> No.3587075

>>3587065
> implying real numbers exist
lolno

>> No.3587079

>>3587065
This is what they want you to believe.
When you deal with infinity the rules go out the window.
0.999... is adjacent to 1.

>> No.3587081

>>3587075
>not using your imagination to do maths

>> No.3587083

>>3587065
Please stop posting.

>> No.3587088

>>3587058
Let A = 1.00..1 and B = 1. What is (A + B) / 2? If such a number exists, then it must be strictly between A and B.

>> No.3587089

>>3587079 When you deal with infinity the rules go out the window
Uhm, no?

>> No.3587100
File: 260 KB, 395x385, hey.png [View same] [iqdb] [saucenao] [google]
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>>3587088
There isn't any since they are adjacent
Also you can't add or substract if there is an infinity of digit

>> No.3587107

pre PhD math here.

All math sheeps shout "0.99999.. =1'

But its really not, the answer is:
0.9999~ is 0.9999~

>hur 1=2 cause its da next posibul answaser

But going in more realistically, 0.9999~ is false by itself.
Infinity is the opium of the math masses.
Grow up.

>> No.3587110

>>3587100
>Addition in an uncountable field - now available as an incomplete operation
Oh this is getting better by the minute

>> No.3587112

>>3587089
Please stop posting.

>> No.3587130

>>3587079
no, they don't. you don't have a proof. the contrary has proof. your superficial appeals lack solid logic and you're too stubborn to accept logic. it's that simple.

>> No.3587143
File: 26 KB, 344x345, 1308747650325.jpg [View same] [iqdb] [saucenao] [google]
[ERROR]

>>3587130
What's more logic:
0 with an infinity of 9 is different of 1 with infinity of 0
Or mathematicians are full of shit and their rules suck

>> No.3587222

>>3587143
seeing as positional notation is a language to express numbers with a set of RULES (like any other language), and violating them (like you're attempting) defeats the purpose, I'd say you're full of shit and lack understanding of the fundamentals
you don't get to change the rules whenever they suit you and claim to be speaking the same language
we're talking about math, not pretend-math

>> No.3587555

>>3586629

And also OP. This is a correct proof. The only part which is not clear is that 0.99999... * 10 = 9.9999... but this can be justified easily using the normal decimal expansion. Indeed, this proof is often adapted to prove the convergence and limit of geometric series.

For those of you who feel you are more "mathematically mature" and who want to use the density of the reals to prove this, you may want to consider something like how we construct the reals in the first place; either Cauchy or Dedekind. One also should note the topological properties of the reals and how they differ from the line with two origins (where this latter structure might represent some line where 0.9999... was not 1, if you'd like).

A slightly more interesting question is: take an arbitrary product of R, and consider the element which takes on the value 0.9999... at every coordinate. Is this equal to the element which takes on 1 at every coordinate? Can you prove this? An easy topological proof exists, but a category theoretical proof is one line if one assumes that 0.9999... = 1 in the one-dimensional case.

>> No.3587642

>>3587107

Jez, I hope this is not what our undergrad programs are doing to students now-a-days. Let's all note that something in and of itself cannot be true or false without a model. Also, a constant, generally speaking, cannot be "true or false." 1 is not true or false, for example.

Let's also note that the definition of equality ( = ) in the case of the reals is an INDUCED equality; the quotient space is, of course, elements which cannot be distinguished by two open sets. In a way, we may think of the reals as the "hausdorff-ification" of the set of all possible decimal strings in a particular way. Kind of a neat idea.

>> No.3587953

two possible substitutes for x. that is all. think quadratic (i.e. quadratic equations can have 2 possible solutions)