1+1=x (say u dunno its2)
1=1/2
so 1/2+1/2+1/2+1/2= 4/2
which is 2
therefore 1+1=2
2006-10-31 20:46:51
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answer #1
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answered by little_devil 2
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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.
2006-11-01 00:58:31
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answer #2
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answered by Dovahkiin 7
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a + a = 2a
so let a = 1
then 1 + 1 = 2*1
1+ 1 = 2 QED
2006-11-01 01:00:12
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answer #3
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answered by bibo 2
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can you prove 1+1 doesnt equal 2?
2006-11-01 00:58:23
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answer #4
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answered by laura 4
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2-1 = 1 therefore 1+1=2
it is a theorem
2006-11-01 00:59:33
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answer #5
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answered by Neo 2
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For a strict mathematical proof you need to take a college course in Elementary Analysis, really. After 1 semester you've proven addition works. You have to show addition on integers is a Division Ring.
(that's all I remember, I took that course in 1971)
2006-11-01 01:00:31
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answer #6
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answered by RichardPaulHall 4
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see your hands one on the left one on the right then count 1,,,2
then 1+1=2
2006-11-01 01:44:02
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answer #7
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answered by Anonymous
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One dollar plus one dollar equals 2 dollars. That's all the proof I need.
2006-11-01 01:00:58
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answer #8
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answered by blue_eagle74 4
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yes
1+1=2 see if you take 1 finger and you take a nother finger and you add them together then yuo get 2
yay doesnt math suck??
2006-11-01 01:01:02
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answer #9
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answered by Anonymous
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No, but it help people to get things done. Just like English and German Etc. it was invented to get things done
2006-11-01 00:59:46
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answer #10
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answered by devsmash 2
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thats wrong
1+1=(2 me you are stupid)
2006-11-01 01:17:39
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answer #11
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answered by Anonymous
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