Proof that 1+1=2 (1 Viewer)

[afton]

Is there a proof that 1+1=2?
or we just accept it as it is?

ps: after Googling I found some proof that
uses Peano postulates, does anyone agree/disagree
with that kind of proof?

 

[Xayma]

I don't think so if I remember correctly Godel's incompleteness theroem prevents it in all but definition.

 

[gordo]

1 = 1
add 1 to both sides

 

[redruM]

thats assuming 1 = 1

 

[gordo]

0=0
and 2 to both sides

 

[Slidey]

The proof of 1+1=2 involves Peano's axioms, as I see you've already noticed. Did you want the proof or not? It is certainly correct and we would not use 1+1=2 if it were not correct.

"The proof starts from the Peano Postulates, which define the natural
numbers N. N is the smallest set satisfying these postulates:

P1. 1 is in N.
P2. If x is in N, then its "successor" x' is in N.
P3. There is no x such that x' = 1.
P4. If x isn't 1, then there is a y in N such that y' = x.
P5. If S is a subset of N, 1 is in S, and the implication
(x in S => x' in S) holds, then S = N.

Then you have to define addition recursively:
Def: Let a and b be in N. If b = 1, then define a + b = a'
(using P1 and P2). If b isn't 1, then let c' = b, with c in N
(using P4), and define a + b = (a + c)'.

Then you have to define 2:
Def: 2 = 1'

2 is in N by P1, P2, and the definition of 2.

Theorem: 1 + 1 = 2

Proof: Use the first part of the definition of + with a = b = 1.
Then 1 + 1 = 1' = 2 Q.E.D.

Note: There is an alternate formulation of the Peano Postulates which
replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the
definition of addition to this:
Def: Let a and b be in N. If b = 0, then define a + b = a.
If b isn't 0, then let c' = b, with c in N, and define
a + b = (a + c)'.

You also have to define 1 = 0', and 2 = 1'. Then the proof of the
Theorem above is a little different:

Proof: Use the second part of the definition of + first:
1 + 1 = (1 + 0)'
Now use the first part of the definition of + on the sum in
parentheses: 1 + 1 = (1)' = 1' = 2 Q.E.D."

Source: http://mathforum.org/library/drmath/view/51551.html

If there's a specific part you need explained, ask.

EDIT: I say 'the proof', but I should be careful. Make that 'a proof'.

 

[dawso]

cant u losers just accept the fact that 1+1=2, i mean, "thats assuming 1=1" wtf??

1 is 1, get over it, fuk...

sincerely, dawso

 

[Euler]

it's done in Principia mathematica by Alfred North Whitehead and Bertrand Russell, though i don't remember which volume it is in.

 

[Archman]

cant u losers just accept the fact that 1+1=2, i mean, "thats assuming 1=1" wtf??

1 is 1, get over it, fuk...

sincerely, dawso

i agree....

 

[Templar]

cant u losers just accept the fact that 1+1=2, i mean, "thats assuming 1=1" wtf??

1 is 1, get over it, fuk...

sincerely, dawso

Go read some other thread then.

 

[paganinio]

Is there a proof that 1+1=2?
or we just accept it as it is?

ps: after Googling I found some proof that
uses Peano postulates, does anyone agree/disagree
with that kind of proof?

okay let me teach you a proof
you have 1 post count now
then you post another thread
you'll find you've got 2 post count
hence 1+1=2

 

[mojako]

okay let me teach you a proof
you have 1 post count now
then you post another thread
you'll find you've got 2 post count
hence 1+1=2

can you trust this forum software?

 

[Slidey]

I see that the Peano Postulates are a recursive axiom set. I also see that the set of natural numbers is incomplete. I aplogise - Xayma (and afton) is correct.

 

[hasterz]

this is the most stupidest thing ive ever read, how can a natural number not be the same as itself??

 

[Slidey]

You only find it stupid because you don't understand it.

Furthermore, whether or not it does indeed equal itself is not of concern. For example, in a similar vein the Riemann Zeta Hypothesis, I think it is, is accepted to be true, however it has not yet been proven. Of importance is not whether or not it is true, but whether or not it can be proven.

 

[paganinio]

we assume 1=1 and add 1 to both sides we get 1+1=2, this is not assuming 1=1, but assuming 1+1=2 itself, that's the problem of this debate

 

[hasterz]

Well obviously all proofs relating to this question will be purely based on definition since the question is basically asking what exaclty is 1 + 1 so If you dont define the number theory your using i cant see how you can prove it

According to the Peano Postulates these are the assumptions you need to make

1 is in N.

If x is in N, then its "successor" x' is in N.

There is no x such that x' = 1.

If x isn't 1, then there is a y in N such that y' = x.

If S is a subset of N, 1 is in S, and the implication

(x in S => x' in S) holds, then S = N.

 

[LoneShadow]

when maths geeks are bored to death they go after proofing that 0=0 [1+1=2]......It's just fkn bullshit. If you are not sure tha 1+1 = 2 after 15 years in a clasroom...go fk urself or ask a lil first grade kid [directed to those bored geeks].

I thought learning more makes u smarter...not dummer.

 

[smallcattle]

OK, you take out one pie from the fridge and place it on the table, then you take out another pie from the fridge and place it onto the table. Now, how many pies do you see???

 

[Xayma]

Yes but this world is a rare example with only 3 spatial dimensions, and around 9 other ones (Super symmetry string theory). You need to prove 1+1=2 in all cases, which is more difficult.

Also you defined 2 as 1+1 not proved it. You can't because it will all come back to you defining 1+1 as 2.