Sythe Users: What Do They Know? Do They Know Things?? Lets Find Out! #7

The overlords in a parallel dimensions where the Shiteian spaceship did not become irradiated are not impressed with the math being taught in their highschool. For example, the following proof is taught, which appears to be OK:
0.99999... = X
9.99999... = 10X
9.99999... -0.99999... = 10X - X
9 = 9X
X = 1
Therefore:
0.99999... = 1

However the out-of-the-box thinking math teacher, Dr. Butt, has also taken to teaching the proof from the other side of the decimal:
...999999 = Y
^ this number has an infinite number of 9's to the left. So its the sum of 9 + 90 + 900 + 9000 + 90000 + ..... to an infinite number of terms.
10*(...999999) = 10Y
...9999990 = 10Y
Note that: Y - 9 = ...9999990
Therefore:
Y - 9 = 10Y
-9 = 9Y
Y = -1
Therefore:
...999999 = -1

This has the overlords very concerned. Help Dr. Butt explain this proof to his overlords.

 

[Fishy D]

This made so much more sense in my head, lol.

What's the overall conclusion, lord?

 

This made so much more sense in my head, lol.

What's the overall conclusion, lord?

Read #5 for hints

 

[Fishy D]

Read #5 for hints

Can I haz your jake the dog minirank?

 

[Deathsnova]

So...how about this weather we're having?

Edit: This is called a 'maelstrom' and its a famous occurance known to happen sometimes in our infamous Australian Summer Storms. Recently, the state in which me and my boy Big Rich both live had whats known as a 'cracker' of a storm. During a maelstrom, up to hundreds of lightning strikes can be felt raining down upon the earth in mere seconds of eachother. Several people have been known to be struck by lightning during these. Side effects of being struck by lightning include loss of IQ, leading many post-lightning victims to go on and vote for labour.

 

So...how about this weather we're having?

Edit: This is called a 'maelstrom' and its a famous occurance known to happen sometimes in our infamous Australian Summer Storms. Recently, the state in which me and my boy Big Rich both live had whats known as a 'cracker' of a storm.

That was a storm? I thought you just farted all the trees over down my street

 

[Fishy D]

That was a storm? I thought you just farted all the trees over down my street

Can I haz that minirank pls?

 

[Time To Buy]

See, the problem here is that Dr. Butt doesn't understand the concept of infinity. Y, 10Y, Y-9 are all the same, infinity.

That's why the proof is wrong. The overlords should execute Dr. Butt

 

If you add 1 to Y you ripple 0s so Y+1=...000=0 meaning Y=-1

 

See, the problem here is that Dr. Butt doesn't understand the concept of infinity. Y, 10Y, Y-9 are all the same, infinity.

That's why the proof is wrong. The overlords should execute Dr. Butt

The numbers are provably different. Just like we have control over the most significant places of the infinite repeating decimal in the top proof, we have control over the least significant places of the infinite repeating decimal in the bottom proof.

If the numbers were the same then for example ...9999991 mod 2 would be the same as ...9999990 mod 2. Will you argue that's the case? There's nothing to stop us constructing these numbers.

Edit: I've posted a sum notation version a couple of posts down.

 

If you add 1 to Y you ripple 0s so Y+1=...000=0 meaning Y=-1

There must necessarily be a 1 in the leftmost position if you do that.

Therefore it's actually 1...000000 = 0

 

Here's another more conventional way to think about it:

 

What exactly are you looking for here? You could do

Y/9 = 1+10+10^2+10^3+...
10Y/9 = 10+10^2+10^3+...
which gives Y = -1 when subtracting, but that's basically what's in the first post

 

What exactly are you looking for here?

Well if the proof is correct then the conclusion is a contradiction.

Explain what's gone wrong or how it can be understood to be correct

 

[Deathsnova]

That was a storm? I thought you just farted all the trees over down my street

Incredibly immature. Also;

Those 3am thread lurks.

 

[Fishy D]

May I haz that minirank now pls SCYF?

 

something to do with p-adics?

also, for

There must necessarily be a 1 in the leftmost position if you do that.

Therefore it's actually 1...000000 = 0

there is no leftmost position? otherwise we could also say 1-0.999... = 0.000...1

 

the answer is jesus

 

[Accounts Shop]

Here's another more conventional way to think about it:

Y is a geometric serie of first term 9 and ratio 10.

10Y is a geometric serie of first term 90 and ratio 10.

Y = 9 * (1 - 10^n+1) / (1 - 10)
Y = 9 - 9*(10^n) / -9
Y = 9/-9 - 9(10^n)/-9
Y = -1 + 10^n

10Y = 90 * (1 - 10^n) / (1 - 10)
10Y = 90/-9 + 10(10^n)
10Y = -10 + 10(10^n)

Y - 9 = -1 + (10^n) - 9
Y - 9 = -10 + 10^n

Y - 9 = 10Y

-1 + 10^n - 9 = -10 + 10(10^n)

-9 = -10 + 10(10^n) + 1 - 10^n

-9 = -10 + (100^n) + 1 - 10^n

-9 = -9 + 10(10^n) - 10^n

-9 = -9 + 10^n * (10 - 1)

-9 = -9 + 10^n * 9

...


no more time to think this through, i'm probably close but so far away

 

[MohtasaUnique]

Sorry sythe, I have a personal policy not to appropriately participate in anything Deathsnova has already marred with his presence. Therefore, I cannot answer your question with impeccable reasoning and excellent vocabulary :c