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Try again - supertramp

Omg!!!

dude how do i play online game here?

dude how do i play online?

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.

this makes no sense what so ever, reducto ad absudum does not make sense at all, 

and how can 1=S(0) anything multiplied by 0 is 0, nothing you explained makes any sense at all, you just proved that you are an idiot, where did you even get this?

bcrekmore:

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.

this makes no sense what so ever, reducto ad absudum does not make sense at all, 

and how can 1=S(0) anything multiplied by 0 is 0, nothing you explained makes any sense at all, you just proved that you are an idiot, where did you even get this?

Rofl imo

the last time i checked, this thread was on russian infantry, though math is a nice subject

[A414A] :(:

Obviously no one cared about Russian Infantry.

lante:

omg,c'mon russian inf is ok if you combinate it with cav and cannons.. evert tried to beat 5 falcs, 30musks 30 strelets and some cav? u dont gonna win

who ever said anything is wrong with russian infantry

bcrekmore:

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.

this makes no sense what so ever, reducto ad absudum does not make sense at all, 

and how can 1=S(0) anything multiplied by 0 is 0, nothing you explained makes any sense at all, you just proved that you are an idiot, where did you even get this?

You just proved your an idiot by believing this pile of bullshit, Well done Moronz and welcome to Agecomm.

unless you have an army of and some skirmishers, or any other infantry calvary, the horses will kill the strelets and cannons easy and then the skirmishers kill the muskets and calvary helps

but, russsian has a horse that is good vs other horses so...

the best russian infantry is the halb they are very strong, but expensive