# Proof that 2+2 = 4

#### Genius Of EPW

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Theorem 1. Two plus two equals four.
Proof of Theorem 1. The set of integers is an (infinite) group with respect to
addition. Since 2 is an integer, the sum of 2 and 2 must also be an integer.
Suppose, for the sake of contradiction, that 2 + 2 < 4. We have 2 > 0.
Adding two to both sides, we get 2+2 > 0+2. Since 0 is the identity element
for addition, we have 2 + 2 > 2. Hence
2 < 2 + 2 < 4
so 2 + 2 must equal 3. Since 3 is prime, by Fermat’s Little Theorem we
have the following for a ∈ Z
+:
a
3−1 ≡ 1 (mod 3)
a
3−1 ≡ 1 (mod 2 + 2)
But
a
3−1 =
a
3
a
=
a × a × a
a
= a × a
and, for a = 2,
2 × 2 ≡ 0 (mod 2 + 2)
since, by the definition of multiplication, 2 × 2 = 2 + 2. So, we have
2
3−1 ≡ 0 (mod 2 + 2)
2
2+2−1 ≡ 0 (mod 2 + 2)
This is a contradiction to Fermat’s Little Theorem, so 2 + 2 must not be
prime. But 3 is prime. Hence 2+2 must not equal 3, and therefore 2+2 ≥ 4.
It remains to show that 2 + 2 is not greater than 4. To prove this we need
the following lemma:
Lemma 1. ∀a ∈ Z, if a > 4, ∃b ∈ Z such that b > 0 and a − 2 = 2 + b.
If a were a solution to the equation 2 + 2 = a, then we would have
a − 2 = 2 + 0. The lemma states that this cannot hold for any a > 4, and so
a = 4, as desired. So, it only remains to prove our lemma.
Aaron Segal, 2010 2 + 2 = 4
Proof of Lemma 1. The proof is by induction over a. Our base case is a = 5.
Let 5−2 = 2+b. Five is the 5th Fibonacci number, and 2 is the 3rd Fibonacci
number. Therefore, by the definition of Fibonacci numbers, 5 − 2 must be
the 4th Fibonacci number. Letting fi denote the ith Fibonacci number, then
we have
fi − fi−1 > 0
for i 6= 2, because f2 − f1 = f0 and f0 = 0, but f1 = 1, and the Fibonacci
sequence is nondecreasing. Hence (5 − 2) − 2 > 0.
Now, suppose that ∃b ∈ Z such that b > 0 and (k − 1) − 2 = 2 + b. We
need to prove that, for some b
0 > 0, k − 2 = 2 + b
0
. Our inductive hypothesis
is equivalent to:
k − 1 − 2 = 2 + b
k − 1 − 2 + 1 = 2 + b + 1
k − 2 = 2 + (b + 1)
Since 1 > 0 and b > 0, we have (b + 1) > 0. Thus, letting b
0 = b + 1, we
have a nonnegative solution to k − 2 = 2 + b
0
, as desired.
By Lemma 1, it is not the case that 2 + 2 > 4. Hence 2 + 2 ≤ 4. We also
have 2 + 2 ≥ 4. Therefore,
2 + 2 = 4

tl;dr: top kek build the wall
Last Edit: Apr 10, 2016, 08:40 pm by Arushi
yo les noobs. There's a difference between an EP playing for his teammates and the teammates playing for the EP. I'm co-leading, organizing every defaults, our "TW dates", strats, etc .. I'm going first when it's tough day in office (people in guild been working 12 jobs that day), and I'm throwing the heals when we do specific tactics. In the first 10 minutes I'm buying the turrets and cata scrolls. Anyway life is tough sometimes but I'm getting paid very well (1 DT per decade). I don't care about having 32 kills, being known, I don't care having movie about me, I want to win. And you know what? I've been winning since 10 years with all of my factions. I'm not here because I'm Swane's best edate. Swane got kicked a couple of times and I've always followed him coz' I like playing with him,

#### Μȓ.ŦαϿöS

• Retired due to Haxs
• Dicks out for my man Harambe who is hiding in a private island with tupac
didnt read 2+2=7 and you cant my mind

#### nebil

• Creepy
• Focus Ur Mind
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I got headache .... too much math for me
One Day U Be a Star

#### ★Trinity★

• ☆God forgives, i don't☆
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Was about to say the same thing ....

#### Teru

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Easy math

#### Damage

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Elementary school maths

Signature by Royal

quit

#### ⋆°🌹 𝔑𝔦𝔞 🌹⋆°

• ♥ мιℓαи'ѕ ♥
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Easy math
Proof that you are a nerd.
♦♢ 𝓜𝓲𝓵𝓪𝓷 𝓘𝓼 𝓜𝔂 𝓟𝓾𝓭𝓭𝓲𝓷  ♦♢
❈𝓣𝓱𝓪𝓷𝓴 𝓨𝓸𝓾 𝓢𝓲𝓼 𝓕𝓸𝓻 𝓣𝓱𝓮 𝓛𝓸𝓿𝓮𝓵𝔂 𝓐𝓻𝓽 𝓘𝓵𝔂𝓼𝓶 ❈
♥ 𝓐𝓻𝓬𝓱𝔂'𝓼 ♥
𝓹.𝓼. - 𝓐𝓻𝓬𝓱𝔂 𝓐𝓚𝓐 𝓟𝓾𝓭𝓭𝓲𝓷 𝓦𝓪𝓼 𝓗𝓮𝓻𝓮

#### 𝔍𝔞𝔰𝔪𝔦𝔫𝔢🎀

• ★Tyrants★
• All snakes don't hiss
Took the words right out of my mouth man

♦Emo♦Ep♦And♦Snow♦Whale♦
Ty Mari, Dendoora, and Leonora

#### Teru

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Proof that you are smart
Fixed that for you

#### ScandaIous

• Done
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Well. I already knew that. Say something new pls

#### ⋆°🌹 𝔑𝔦𝔞 🌹⋆°

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Fixed that for you so I can feel special

Oooo ok
♦♢ 𝓜𝓲𝓵𝓪𝓷 𝓘𝓼 𝓜𝔂 𝓟𝓾𝓭𝓭𝓲𝓷  ♦♢
❈𝓣𝓱𝓪𝓷𝓴 𝓨𝓸𝓾 𝓢𝓲𝓼 𝓕𝓸𝓻 𝓣𝓱𝓮 𝓛𝓸𝓿𝓮𝓵𝔂 𝓐𝓻𝓽 𝓘𝓵𝔂𝓼𝓶 ❈
♥ 𝓐𝓻𝓬𝓱𝔂'𝓼 ♥
𝓹.𝓼. - 𝓐𝓻𝓬𝓱𝔂 𝓐𝓚𝓐 𝓟𝓾𝓭𝓭𝓲𝓷 𝓦𝓪𝓼 𝓗𝓮𝓻𝓮

#### 🎧 F Λ Y Ɛ

• ayy
What the fuck
I feel like you have too much time on your hands...
Love is not just a verb, it's you looking in the mirror.

• hi
• me bestest

#### Genius Of EPW

• [Protected from EPW Ban]
• [Only VIP EPW forum users can see this text]
• Characters: Cate
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yo les noobs. There's a difference between an EP playing for his teammates and the teammates playing for the EP. I'm co-leading, organizing every defaults, our "TW dates", strats, etc .. I'm going first when it's tough day in office (people in guild been working 12 jobs that day), and I'm throwing the heals when we do specific tactics. In the first 10 minutes I'm buying the turrets and cata scrolls. Anyway life is tough sometimes but I'm getting paid very well (1 DT per decade). I don't care about having 32 kills, being known, I don't care having movie about me, I want to win. And you know what? I've been winning since 10 years with all of my factions. I'm not here because I'm Swane's best edate. Swane got kicked a couple of times and I've always followed him coz' I like playing with him,