AOE3 Forums

[A414A] LorèneJtm:

Retreat and make culvs.

I just surrounded you, what do you do?

[A414A] LorèneJtm:

I never let you do that.

I just surrounded you, you die.

Sid the Great:

A 414 will bring his lances to surround You. Just like Caesar did in Gaul- His cavalry surrounded the Gauls that surrounded his infantry!

I'm in A414A, so is this like Infinite Surrounding of each-other??

bcrekmore:

i think he is talking about you  a414a

A414A is a clan noob.

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

2+2=4

Who care's who right, just get over it the world doesn't need to know.

chaseehat:

2+2=4

Who care's who right, just get over it the world doesn't need to know.

2+2=4 is more important in some aspects.

Except 2+2 can equal 5!!!!!!!!!!!!!

1: There exists a natural number 0
2: Every natural number has a successor
3: Distinct natural numbers have distinct successors (i.e. S(x) = S(y) ⇒ x=y)
4: No natural number has 0 as its successor (i.e. ∀x, S(x) ≠ 0)
5: Any set of natural numbers that contains 0 and is closed under succession contains all natural numbers (i.e. for any set K, (0∈K ∧ (∀x (x∈K ⇒ S(x)∈K))) ⇒ ∀x (x∈K)).

We also have the recursive definition of addition -- addition is the unique function +:N → N with:

x+0 = x
x+S(y) = S(x+y)

And finally, the definitions of the numerals other than 0:

1 = S(0)
2 = S(1)
3 = S(2)
4 = S(3)
5 = S(4)
...

And so on. So, we wish to establish that 2+2 ≠ 5. Note that:

2+2
= 2+S(1) (def. of 2)
= S(2+1) (def. of +)
= S(2+S(0)) (def. of 1)
= S(S(2+0)) (def. of +)
= S(S(2)) (def. of +)
= S(3) (def. of 3)
= 4 (def. of 4)

So it remains only to establish that 4≠5. To do this, suppose the contrary, that 4 = 5. Then we have:

4=5
S(3) = S(4) (def. of 4 and 5)
3 = 4 (axiom 3)
S(2) = S(3) (def. of 3 and 4)
2 = 3 (axiom 3)
S(1) = S(2) (def. of 2 and 3)
1 = 2 (axiom 3)
S(0) = S(1) (def. of 1 and 2)
0 = 1 (axiom 3)
0 = S(0) (def. of 1)

However, 0≠S(0) (axiom 4), so by reductio ad absurdum, it follows that 4≠5 and thus 2+2≠5. Q.E.D.

2+2=5 in the novel 1984 though, can't disprove that.

A414A l Ichigo1uk:

chaseehat:

2+2=4

Who care's who right, just get over it the world doesn't need to know.

2+2=4 is more important in some aspects.

Except 2+2 can equal 5!!!!!!!!!!!!!

 

1: There exists a natural number 0
2: Every natural number has a successor
3: Distinct natural numbers have distinct successors (i.e. S(x) = S(y) ⇒ x=y)
4: No natural number has 0 as its successor (i.e. ∀x, S(x) ≠ 0)
5: Any set of natural numbers that contains 0 and is closed under succession contains all natural numbers (i.e. for any set K, (0∈K ∧ (∀x (x∈K ⇒ S(x)∈K))) ⇒ ∀x (x∈K)).

We also have the recursive definition of addition -- addition is the unique function +:N → N with:

x+0 = x
x+S(y) = S(x+y)

And finally, the definitions of the numerals other than 0:

1 = S(0)
2 = S(1)
3 = S(2)
4 = S(3)
5 = S(4)
...

And so on. So, we wish to establish that 2+2 ≠ 5. Note that:

2+2
= 2+S(1) (def. of 2)
= S(2+1) (def. of +)
= S(2+S(0)) (def. of 1)
= S(S(2+0)) (def. of +)
= S(S(2)) (def. of +)
= S(3) (def. of 3)
= 4 (def. of 4)

So it remains only to establish that 4≠5. To do this, suppose the contrary, that 4 = 5. Then we have:

4=5
S(3) = S(4) (def. of 4 and 5)
3 = 4 (axiom 3)
S(2) = S(3) (def. of 3 and 4)
2 = 3 (axiom 3)
S(1) = S(2) (def. of 2 and 3)
1 = 2 (axiom 3)
S(0) = S(1) (def. of 1 and 2)
0 = 1 (axiom 3)
0 = S(0) (def. of 1)

However, 0≠S(0) (axiom 4), so by reductio ad absurdum, it follows that 4≠5 and thus 2+2≠5. Q.E.D.

1. That's just a fancy way of saying What I said

2. QED goes on the line below the proof

3. Please use set symbols that make sense, wtf is  ∀and ∧? (for someone that hasn't done Uni maths I don't expect to know much)

I smell that a=b, b=0 proof where one line isn't right, and I'm quite sure 0 isn't a natural number

There is only 1 true answer:

Who cares?