Mathematical proof that 2 = 1

[Pilchard123]

I love this, it's great for confusing people.

First:
Let A = B

Then, multiply by A:

A^2 = AB

Subtract B^2:

A^2 - B^2 = AB - B^2

Factorise:

(A+B)(A-B) = B(A-B)

Divide by (A-B):

A+B = B

Since A = B, then B = A, so substitute A for B:

A+A = A, or 2A = A

2 = 1

 

What's wrong?

[annikk.exe]

Solution:

(click to show/hide)

This step:

Divide by (A-B):

If A = B, then A - B = 0.


So we can rewrite as:

Divide by 0

Which obviously doesn't work.  :>

Here's another one.

Imagine the number 0.99999999999999.... with 9's recurring into infinity.

I propose that 0.999... = 1

Sounds counterintuitive?


Think about it this way.
Imagine a "one-third" represented as a fraction:




If we multiply one-third by 3, we get 1.  Right?


* 3 = 1

Right...?



So how do we represent in decimals?

It's 0.3333333333333... recurring.

If we multiply by 3, we get:

0.99999999999.... recurring.


Therefore, 0.999999999.. recurring to infinity, is equal to 1.
They are the same number.

[Pilchard123]

You can do that with ninths, too. 2A = A does work, however, if A = B = 0.

[killybilly]

Okkkkk, im confused.... ALOT!


Whooops bumped into a over 120 days old topic.........

[AWS]

hahahaha!!!!
wow.

no wonder i was 2nd bottom set for maths at school.
i can paint though
lol

[Aino]

Seriously Pilchard, what have you done?! This is madness D:

[Pilchard123]

Divided by zero.

If A = B, then A-B=0

Dividing by A-B is the same as dividing by zero.

[Aino]

Divide by zero? I don't understand... *input another meme here*

[Sniped50]

Aino, think about what 1 divided by 0 means.

It basically is asking 'How many zeroes go into a one?'. And since you could fit an infinite amount of zeroes in to a one (because you can never reach it if you tried), the answer is basically infinity. That's why it doesn't work... 

Also, Pilchard, may I ask what the answer would be if you did 0 divided by 0?

I mean, because you're dividing by zero, the answer is always infinity. Right? However, you are also dividing into zero, so the answer is always zero. Right?

>PARADOX DETECTED
>YOU WILL DIE, HUMAN!
*argh*
*die*
>PHASE 1 COMPLETE
>PREPARING FOR PHASE 2

[Aino]

I know that dividing by 0 means infinite... I got some experience from that god damned coding