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2006-08-24 11:39:01 · 23 answers · asked by Tyler L 1 in Education & Reference Homework Help

23 answers

1 + 1 = 2

Here's the proof for it; you might be interested:

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.

2006-08-24 11:40:57 · answer #1 · answered by Dan 4 · 0 0

1+1=2

2006-08-24 18:47:23 · answer #2 · answered by r 3 · 0 0

1+1=2

2006-08-24 18:41:07 · answer #3 · answered by Fourtonfour 3 · 0 0

2

2006-08-25 23:24:08 · answer #4 · answered by krazymagex 2 · 0 0

2

2006-08-24 18:42:40 · answer #5 · answered by Anonymous · 0 0

= 11

2006-08-24 18:40:12 · answer #6 · answered by Big R 6 · 0 0

1 +1=2 dumbo.

2006-08-24 18:42:13 · answer #7 · answered by kimiko0685@sbcglobal.net 1 · 0 0

3?? no thta 1+1+1

2006-08-24 18:41:36 · answer #8 · answered by nas88car300 7 · 0 0

Lets assume you are NOT using the decimal system and you are using the Binary system, then

1 + 1 = 10 (base 2)

2006-08-24 21:31:58 · answer #9 · answered by alrivera_1 4 · 0 0

1 apple + 1 apple = constipation
1 sex + 1 sex = pregnancy
1 star + 1 star = hollywood
1 ball + 1 ball = dick_head
1 penny + 1 penny = bankruptcy

2006-08-24 18:46:24 · answer #10 · answered by Busy Diyosa 5 · 0 0

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