# 1=2

A baffled mathematician

One of the great mysteries of the universe is that 2 is the same as 1.

## Baffled Scientists

The mystery of 1 = 2 has baffled scientists and mathematicians for thousands of years. The evidence is clear that 2 is 1 and 1 is 2; however, some scientists dispute this fact because their moms believed in 2, and they wanted to keep their mothers happy.

Since 1 = 2, we can assume that 2 = 1. This causes all sorts of problems somehow. But

1. Nobody cares and
2. Mathematicians are too lazy to figure these problems out.
3. Some people just want to defy everything

## 1=2 graph

You can clearly see in the following graph that for most random points plotted, 1 = 2.

## Proof

• Everyone knows this:
${\displaystyle {\frac {-1}{1}}={\frac {1}{-1}}}$
• Now we will square root both sides:
${\displaystyle {\sqrt {\frac {-1}{1}}}={\sqrt {\frac {1}{-1}}}}$
• Now we break up the roots:
${\displaystyle {\frac {\sqrt {-1}}{\sqrt {1}}}={\frac {\sqrt {1}}{\sqrt {-1}}}}$
• The square root of a negative 1 is i and the square root of 1 is 1. In other words:
${\displaystyle {\frac {i}{1}}={\frac {1}{i}}}$
• Now we divide the entire thing by 2:
${\displaystyle {\frac {i}{2}}={\frac {1}{2i}}}$
• Now let's add ${\displaystyle \textstyle {\frac {3}{2i}}}$ to make the math easier.
${\displaystyle {\frac {i}{2}}+{\frac {3}{2i}}={\frac {1}{2i}}+{\frac {3}{2i}}}$
• Now we can multiply the entire thing by i:
${\displaystyle i\left({\frac {i}{2}}+{\frac {3}{2i}}\right)=i\left({\frac {1}{2i}}+{\frac {3}{2i}}\right)}$
• So now we expand this beast:
${\displaystyle {\frac {i^{2}}{2}}+{\frac {3i}{2i}}={\frac {i}{2i}}+{\frac {3i}{2i}}}$
• We know that the square root of -1 is i, so i2 must be -1:
${\displaystyle {\frac {-1}{2}}+{\frac {3i}{2i}}={\frac {i}{2i}}+{\frac {3i}{2i}}}$
• Now we simplify the i's
${\displaystyle {\frac {-1}{2}}+{\frac {3}{2}}={\frac {1}{2}}+{\frac {3}{2}}}$
• Let's calculate this thing:
${\displaystyle {\frac {2}{2}}={\frac {4}{2}}}$
• And so
${\displaystyle 1=2}$

## Another Proof

Let a = b

now, a2 = b2 = ab

a2 - b2 = a2 - ab

(a+b)(a-b) = a(a-b)

a+b = a

a+a = a

2a = a

2 = 1

## Yet Another Proof

• This is the expansion of the natural logarithm of 2
${\displaystyle \log 2=1-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-{\frac {1}{6}}+\cdots }$
• Now separate out the even-numbered fractions from the odd-numbered ones
${\displaystyle \log 2=\left(1+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{7}}+\cdots \right)-\left({\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{6}}+{\frac {1}{8}}+\cdots \right)}$
• a-b=a+b-2b, so
${\displaystyle \log 2=\left(1+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{7}}+\cdots \right)+\left({\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{6}}+{\frac {1}{8}}+\cdots \right)-2\,\left({\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{6}}+{\frac {1}{8}}+\cdots \right)}$
• Now simply combine the first two terms and distribute the 2 throughout the third term
${\displaystyle \log 2=\left(1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+{\frac {1}{5}}+{\frac {1}{6}}+\cdots \right)-\left(1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+{\frac {1}{5}}+{\frac {1}{6}}+\cdots \right)}$
• The two remaining terms are the same, so
${\displaystyle \log 2=0}$
• Now since e0=1, log 1=0 also
${\displaystyle \log 2=\log 1}$
• Now just take the exponential of both sides
${\displaystyle 2=1}$

“But maybe log2 isn't 0”

~ Mathmatician on this proof

${\displaystyle 2\log 2=\log 2}$

divide by log 2

${\displaystyle 2=1}$

## Even More Perfectly Correct Proof

• Let's assume that 1=2
${\displaystyle 1=2}$
• Since we asumed that 1=2 we can replace 1 with 2
${\displaystyle 2=2}$

And since 2=2 is correct, our assumption that 1=2 must also be correct

## Yet Another Another Proof (probably the simplest)

• We all know that 0 = 0, right?

0 = 0

• Any number multiplied with 0 equals 0.

1 × 0 = 2 × 0

• Now we simplify the operation.

1 = 2

Simple enough, right?

Note: When simplifying, be careful when you divide by zero. The effects could be devastating.

## Not Convinced?

We can state that anything to the power of zero will always equal 1, any given number0 = 1, so working backwards, we can logicaly state that ${\displaystyle \textstyle {\sqrt[{0}]{1}}}$ = any given number. Now after much thinking and unnecessary government funding, top mathematicians can firmly state that numbers 1 and 2 are in fact "any given numbers". Therefore, we can definitively state that ${\displaystyle 1={\sqrt[{0}]{1}}=2}$.

## Still Not Convinced?

And for you die-hard zerodoesnotequalone-ists, one can convert from a base 0 number system. Number systems always have a maximum value of the number to the power of ${\displaystyle n-1}$ in each place. In any given place, we can see a 1 as the first integer available in that place. Since in the first place, ${\displaystyle 0^{n-1}=0^{1-1}=0^{0}=0}$, we can fill this with a 1. If we move over one place, we get ${\displaystyle 0^{2-1}}$ which is also 0. Since increasing one integer value increased the value by 0 when converted back to a base 10 format, we can see that ${\displaystyle 0=1}$. This also means that every whole number equals 0. However, since every irrational and decimal number can be expressed in similar terms, it can be concurred that every number must logically = 0. Since every number = 0, and ${\displaystyle 1=0}$, every number equals 1, and thus ${\displaystyle 2=1}$.

## Not Convinced Yet?

The principle of MI is very useful. It can be used to prove lots of things!

• Theorem: A positive integer n is equal to any positive integer which does not exceed it.
• Proof by induction:
Case ${\displaystyle n=1}$. The only positive integer which does not exceed 1 is 1 itself and ${\displaystyle 1=1}$.
Assume true for ${\displaystyle n=k}$. Then ${\displaystyle k=k-1}$. Add 1 to both sides and get
${\displaystyle k+1=k}$
• Corollary: All numbers are equal.
• Proof:
Since from above all numbers are equal to the number not exceeding itself it follows that any number larger than a given number must equal the given number.
${\displaystyle k+1=k}$
Thus by reflexivity of the equality relation
${\displaystyle k=k+1}$
Thus for any given number ${\displaystyle k}$ there exists a number exactly one larger than ${\displaystyle k}$ that is its equal. Letting ${\displaystyle k=1}$,
${\displaystyle 1=2}$

See now you know the secrets of math.....

## Chuck Norris' demonstration

The final demonstration...

 This man insists there's one finger. “How many fingers do you see?” What you see think you see Chuck Norris showing. “One!?...”~ You, quaking Your face, in front of Norris “NO!!!”~ Chuck Norris, teaching math before give a Roundhouse Kick on your face Norris talk, listen you. “That's two... tchwo, THAT'S TCHOWWAAHHH!!!”~ YOU, five teeth left Improved View by RHK

### Criticism to Chuck Norris' Proof

• "Well, he didn't really prove anything, besides Chuck Norris is a weak fucker and ev"

(unfortunately the author of comment died half way through from unknown causes, though it's believed that he died of complications resulting from a round house kick)

## Effects of 1=2

A fuckton of confused people

### Winston Churchill is a carrot

• Winston Churchill has 0 leafy tops. But 1=2, and subtracting 1 gives 0=1. Therefore, Churchill has 1 leafy top.
• Churchill has 2 arms. We've shown that 0=1—now if you multiply by 2, 0=2. Churchill has 0 arms.
• Take Churchill's waist size in inches. Let it equal x. Now, multiplying the previous equation 0=1 by x gives 0=x. So, Winston Churchill tapers to a point.
• Take the wavelength of any photon of light emitted from Churchill. Let it equal y. By a process demonstrated earlier, 0=y. Now take a previously-used equation, 0=1, and multiply it by 640nm:
${\displaystyle 0=640\,{\text{nm}}}$
But 0=y:
${\displaystyle y=640\,{\text{nm}}}$
So the wavelength of any photon of light emitted from Churchill is 640nm, a bright shade of orange.

Winston Churchill has no arms, a leafy top, he tapers to a point and is orange. Winston Churchill is a carrot. The implications for vegetable rights are astounding.

### In class, your tests count twice

• If you studied for one day, you really studied for two days.
• If you lost your study packet, you really lost it twice.
• If you forget the answer to one question, you really forgot the answers to 2 questions.
• If you got a 64% on the test, then you really got a 128%.
• If you cry yourself to sleep for one night, you really cried yourself to sleep for two nights.

### 6*9=42

• This is to be proven:
$\displaystyle 6\cdot9\overset{\scriptsize{?}}{=}42$
• Let's look closer at that 9...
$\displaystyle 6\cdot(8+1)\overset{\scriptsize{?}}{=}42$
• Since 1=2, 8+1=8+2=10:
$\displaystyle 6\cdot10\overset{\scriptsize{?}}{=}42$
• 6*10=60=24+2*18, so
$\displaystyle 24+2\cdot18\overset{\scriptsize{?}}{=}42$
• But 2=1
${\displaystyle 24+18=42}$

Thus, the ultimate problem to Life, The Universe and Everything is the ultimate answer to Life, The Universe and Everything.

### Therefore, Everything=Everything Else

We know that 1=2, from this we can derive that any two values are equal

${\displaystyle 1=2}$
• Now, lets add 1 to both sides of the equation.
${\displaystyle 2=3}$
• Notice that both equations contain a common value of two, this means that:
${\displaystyle 1=2=3}$
• Therefore: 1 = 3, this pattern can then be continued:
${\displaystyle 1=2=3=4=5=6=7\cdots }$
• This can also be done in reverse:
${\displaystyle \cdots -5=-4=-3=-2=-1=0=1=2}$
• This law also applies to fractions:
${\displaystyle 0=1=2=3=4=5=6=7=8}$
• Now we divide everything by 8
${\displaystyle {\frac {0}{8}}={\frac {1}{8}}={\frac {2}{8}}={\frac {3}{8}}={\frac {4}{8}}={\frac {5}{8}}={\frac {6}{8}}={\frac {7}{8}}={\frac {8}{8}}}$

So now we can see that all numbers are equal to one another. This means that there will never be any need for the ≠ sign. there will, however, be need for a lot of cake.

### Alcohol's Law

The whole rule of 1=2 is the rule of beer. You cannot have one, but must have two, and by having two you must have 3. Soon enough you will end up with the Alcohol's Law of the hangover theory.

But wait, the hangover theory is useless once you divide by bacon + egg + roll = a heart attack on a plate. The heart attack theory is then also calculated due to grease + mass - no of beers. If this is below 0, an increase to bacon, egg or roll must take place. If above 0, increase the beer load. Once you reach a suitable level of 0, then you will be able to achieve a high level drunkeness with a 0 risk of a hangover.

### Other effects

• You have one cow.
• 2+2=2+1+1=2+2+1=5. Thus, 2+2=5. (For extremely small values of 2.)
• When I have $1 in my bank account, I actually have$2.
• When something costs $1, it really costs me$2.
• "2 for 1" sales are the ultimate in deceptive marketing strategies.
• Finger counting is fundamentally flawed.
• "One-potato-two" is entirely fruitless.
• The phrase "killing two birds with one stone" should be reconsidered.
• The expression "When you've seen one, you've seen them all" is literally true in all circumstances.
• People only have 1 eye, 2 belly buttons, 1 arm and 1 leg.
• Unfortunately, women have 2 mouths, which explain why they talk too much.
• I only have 1 ear, which explains why I only hear half of what my wife says. And since she has 2 mouths, I really only hear a quarter of what she's saying.
• Wikipedia's [1] page should redirect to [2].
• You actually huffed 2 kittens, not 1. (Even though you didn't inhale).
• The Count from Sesame Street represents the pinnacle of immorality.
• By purchasing one meal at an all-you-can-eat buffet, you actually purchased more-than-you-can-eat.
• That's okay, though, because if 1=2=2(1), then you also ate 2(all-you-can-eat).
• Everything=cake
• But THE CAKE IS A LIE, so cake=lie.
• Therefore Everything=lies.