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/sci/ - Science & Math

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14635023 No.14635023 [Reply] [Original]

>9.99999999999999999999...... = 10 because..... because it just does okay?!?!

>> No.14635025

1/3 * 3 = 1

>> No.14635034

>>14635025
>1/3
not a number

>> No.14635039

>>14635034
https://en.wikipedia.org/wiki/Rational_number

>> No.14635051

>>14635025
1/3 =/= .333...

>> No.14635053

>>14635051
prove it

>> No.14635099

You see a walk in front of you. You walk towards the wall. Every time you cover 90% of the distance, your body is magically re-scaled so that walking the remaining distance feels the exact same as the first time, and this process repeats. You are doomed to only walk 90% of each interval, essentially doing the exact same task forever. Will you ever reach the wall? Is this process the same as simply walking and reaching the wall at a constant pace? Here is where you say “at infinity” and assume that an infinite process has been completed. But that just transfers the power of infinity to the walker. Can an unstoppable force defeat an immovable object? Can an infinite walker complete an infinite process? “0.999… = 1” retards simply prefer one infinity and ignore the other, and because they don’t actually understand actual infinities, they don’t care if they don’t know what they’re talking about. Infinity works in mysterious ways

>> No.14635114
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14635114

>>14635099

>> No.14635128

>>14635053
.333... Does not and cannot exist, as that which is defined as a never ending process is not a thing that at a given time can exist as a thing that is defined as an ended item, such as 1. 1 is not a never ending calculating process.

(.333... + .333... + .333... = .999...)

.999... Is defined as a never ending calculating process

Therefore .999... Cannot possibly be equivelent to 1

>> No.14635138

>>14635128
>a never ending process
what “process” is going on in .333…? are you saying you think the threes are like having a chemical chain reaction to constantly spawn more 3’s? or are the dots like a little choo choo train always burning diesel to keep chugging to the right to exhaust more and more 3s on its little train track?

>> No.14635152

[math]0.111... = sum_{i=1}^\infty \left(\frac{1}{10}\right) = \frac{1/10}{1 - 1/10} = \frac{1}{9}[/math]

>> No.14635155

>>14635152
oops.
[math]0.111... = \sum_{i=1}^\infty \left(\frac{1}{10}\right)^i = \frac{1/10}{1 - 1/10} = \frac{1}{9}[/math]

>> No.14635189

>>14635099
I think it's less about considering the infinityness and more just taking at face value:

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

1/3 must equal .333...

Therefore .333... + .333... + .333... must equal 1.

How come the fraction works seamlessly 1/3, 3/3, 1

But the decimal seems to have this akwardness?

>> No.14635197

>>14635138
.333... implies a never ending process does it not?

There is never enough 3's to add on the end. This symbol of notation represents .333... 3's will never stop being added to the end.

There is no end of .333...

It is not finite. It therefore is an ongoing process, not a completed entity object thing.

>> No.14635208 [DELETED] 

>>14635189
because decimals are just another notation for fractions

>> No.14635224

>>14635128
>.999... Is defined as a never ending calculating process
prove it

>> No.14635231 [DELETED] 

>>14635197
>does it not?
it doesn't
it's length is inf from the get go

>> No.14635237

>>14635197
>does it not?
it doesn't
its length is inf from the get go

>> No.14635262

https://www.youtube.com/watch?v=sVxJ016xb4Q

>> No.14635263

>>14635023
This is the dumbest debate ever. 9.99999999... is not in any way shape or form a realistic number. It has zero uses other than this stupid debate. Numbers aren't even real anyways, they're shit made up by man.

>> No.14635267

What does "......" mean? Until you specify it, all we know is
9.99999999999999999999...... [math]\in[/math] [9.99999999999999999999, 10]

>> No.14635283

>>14635237
>its length is inf from the get go
Inf by deffintion does not and cannot exist. If it did, it wouldn't be inf

>> No.14635287

>>14635224
>>.999... Is defined as a never ending calculating process
>prove it
The deffintion of "..." Is: never ending.

There is nothing more to prove, thats it.

>> No.14635299

>>14635023
s = 9.999 ...
10s = 99.999 ...
10s - s = 90
9s = 90
s = 10
q.e.d.

>> No.14635336

>>14635283
what definition are you referring to? can you give me a reference to a math text that contains whatever definition you are using?

>> No.14635342

>>14635263
You are shit made up by your parents.

>> No.14635349

>>14635287
it's static
try again

>> No.14635352
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14635352

>>14635267
It is defined, you are simply ignorant and arrogant to think you know best. There's no need to reinvent the wheel.
>what is an infinitely repeated digit sequence?
https://en.wikipedia.org/wiki/Repeating_decimal#Converting_repeating_decimals_to_fractions

>> No.14635374

>>14635336
"Infinity is that which is boundless, endless, or larger than any natural number."

>> No.14635386

>>14635349
How so?

If .9999999 is bigger than .99999

And .9999999999999999 is bigger

If there are differences between this

.99999999999999999999999999999999999


.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

The idea of .999... Is certainly not static, as you claim, if the idea of it is more and more .9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999s

More and more and more and more and more.


It's certainly not static!

1 is static.


Anything with ..... Is the very meaning of continual action.

Or else .999 itself would be good enough. Or .9999999999

As long as you admit a difference by adding another 9.

And ....... Means adding more.

Then .999.... Cannot = 1

>> No.14635392
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14635392

>>14635352
From this wiki page, there is also the following reference
>Beswick, Kim (2004), "Why Does 0.999... = 1?: A Perennial Question and Number Sense", Australian Mathematics Teacher, 60 (4): 7–9

>> No.14635406

>>14635386
You don't understand the math symbols, which is why your reasoning is flawed. Look up the wiki page and the reference that have been posted above. It should become clear to any kindergarten student, including you.

>> No.14635410

>>14635386
0.999... is static, the length is aleph_0 from the get go.
Your naive cartoon vision of a diesel engine chugging along is ridiculous. Embarrassing even.

>> No.14635421

>>14635352
It doesn't say "infinitely repeated" anywhere in the OP. You just assumed it.

>> No.14635424

Does it really take so much brain power to see that 1/3 is more than 0.333..
It just does not translate into decimals, end of story

>> No.14635431

>>14635424
Is it?
1/3 > 0.33325349258435
1/3 < 0.3338545345

>> No.14635441

>>14635421
It is one of the possible notations. Again, see the wiki page https://en.wikipedia.org/wiki/Repeating_decimal#Notation

Why do you refuse to educate yourself?

>> No.14635452

>>14635392
he could have just said this part
>the sum 0.9 + 0.09 + 0.009 + ... (which is 0.999...) becomes arbitrarily close to 1
and deleted the rest of the paper

>> No.14635453

>>14635424
Does it really take so much brain power to see that you are dumb
It just does not translate to intelligence, end of story

>> No.14635459

>>14635441
>This notation introduces uncertainty as to which digits should be repeated and even whether repetition is occurring at all, since such ellipses are also employed for irrational numbers; π, for example, can be represented as 3.14159....
Nice self-pwn.

>> No.14635461

>>14635452
there are multiple ways to get to the result, continue reading
and see also geometric series derivation from >>14635155
based on
https://en.wikipedia.org/wiki/Geometric_series#Sum

>> No.14635462

>>14635459
All the digits are the same in the op. It's all 9. There's no uncertainty. You are only pwning yourself by refusing to learn proper maths.

>> No.14635467

>>14635452
>he
you mean she

>> No.14635469

>>14635461
author gives lots of proofs she admits belong in scare quotes and is confused why students reject them

>> No.14635472

>>14635462
How do I know the digits don't continue 9.999999999999999999996783673456354654?

>> No.14635480

>>14635472
>i don't understand notation
because that's not what ellipsis represents in the context of repeating decimals

>> No.14635483

>>14635452
also even that is badly put
here's how the paper could be rewritten:
>By 0.999... we mean the real number which the numbers 0.9, 0.99, 0.999, ... become arbitrarily close to, which is 1.

>> No.14635485

>>14635480
OP wasn't talking about repeated decimals. OP was obviously talking about the important number 9.999999999999999999996783673456354654. Educate yourself.

>> No.14635486

>>14635480
The example 1/3 = 0.(3) = 0.333... is even given in the second row of that table.

>> No.14635488

>>14635485
The proper way of doing math doesn't care about your feelings, chud.

>> No.14635489

>>14635485
Fun fact: this number is related to thrembo.

>> No.14635717

>>14635410
Then .999.... Does not mean adding infinite amount of 9's

It either does mean that, or it does not. If it does, then that number does not equal 1, that is plain to see.

>> No.14635721

>>14635483
There is no arbitraryness in the perfect equality seeking exacting realm of pure and true Math

>> No.14635848

>>14635374
Good job, you can't form a bijection with the amount of 3s in 0.333... and any finite natural, any other objections?

>> No.14635854

>>14635023
Anyone who saves your op image to their computer has a mental illness, get yourself checked op

>> No.14635957
File: 164 KB, 957x931, Screenshot_20220708-125814_Samsung Internet.jpg [View same] [iqdb] [saucenao] [google]
14635957

>>14635854
>Anyone who saves your op image to their computer has a mental illness, get yourself checked op

>> No.14636127

>>14635717
>adding
it's not a process chugging along, it's the result
it's static

>> No.14636172

>>14635717
It doesn't.

>> No.14636200

>>14635717
1/2+1/4+1/8... = 1

Therefore 1 doesn't exist.

>> No.14636227

>>14635483
Unfortunately saying arbitrarily close is still hand-wavey and not precise.

The real explanation has to do with trying to find a number between 0.999... and 1. Since we don't know what that number is, it's easier to define a Cauchy sequence |x_m - x_n| = (1-9/10), (1-99/100), ... And show at some point N > n,m, there exists some number that |x_m - x_n| < that number (basically the tail end of the differences disappears or is very tiny).

Well, if we fix x_m = 1, then |x_m - x_n| = (1/10), (1/100), (1/1000)... So for large enough N, we want to show 1/(10)^N goes to 0.

>> No.14636293

>>14636227
>Since we don't know what that number is
We don't know what it is because it doesn't exist. There is no number in-between those two values

>> No.14636299

>>14636293
Yes that's what I just proved. You can't just say something and believe it to be true without proving it; it doesn't work like that.

>> No.14636309

>>14636299
That's where you're wrong bucko. It's intuitive that 1 - 0.999... comes out to 0, because it doesn't make any sense that there's any kind of number that can fit in that gap.
Proving stuff is for nerds

>> No.14636333

>>14635717
>that is plain to see.
Do people here unironically not know what convergent sequences are?
Is it underageb&s?

>> No.14636341

>>14635336
>what definition are you referring to?
none. he's referring to a "deffintion", whatever that is.

>> No.14636344

>>14636333
A few here are not yet in 6th grade. The others are pedos trying to groom them by trolling.

>> No.14636509

>>14635023
do NOT reply to /qa/ soijak spammers
do NOT bump /qa/ soijak spammers

>> No.14636526

>>14636341
By definition infinity cannot exist.

That which exists, is by definition finite.

If an "infinity" could exist, it would be finite, therefore it would not be an infinity.

>> No.14636545

>>14636526
Please translate into non-autistic