What is one plus one?

• An elementary school pupil: 2.
• A middle school pupil: 2.
• A hich school student: 2.
• A normal college student: 2.
• A college student with computer science in the cirriculum: 2 or 10. 2 in decimal, %10 in binary.
• A mathematician: 2 or 0. 2 if the numers belong to the natural, whole, rational, real or complex numbers. 0 if they are in the group Z₂. The latter can be seen as the cardinality of a family where both parents died before they had any children.
• A logician (who overheard the mathematician): 1, because in boolean algebra, the '+'-symbol represents a logical or-relation.
• Peano (The Logician):

  1	(1)	∀x ∀y (x + S(y))	=	S(x + y)	Premiss (Peano 4)
  2	(2)	∀x (x + 0)	=	x	Premiss (Peano 3)
  1	(3)	∀y (S(0) + S(y))	=	S(S(0) + y)	1 ∀E
  1	(4)	S(0) + S(0)	=	S(S(0) + 0)	3 ∀E
  2	(5)	S(0) + 0	=	S(0)	2 ∀E
  1,2	(6)	S(0) + S(0)	=	S(S(0))	5,4 =E

• A C++-programmer: 2, unless the numbers are of an unusual type with operator overloading on the '+'.
• A Java programmer: 2 or 11. It depends on whether 1 and 1 are int or String.
• A conspiracy nerd: In the reality I think I live in it has always been 2, but I'm not sure. Somebody may have hacked reality to make us believe it to be 2, or hacked my brain to make it true in my experiences.
• A five-year old kid, smarter than most other people: I don't know! If I have a stone and add another stone, then I have two stones, but if a brook flows into another brook... I only have one brook!
• Excecutive summary: 0, 1, 2, 10 or 11 depending on level of education, individual choices, number base, number system, algebraic structure, operator overloading and language syntax. I suggest you answer two, otherwise people will think you are paranoid or naïve.

(C) Marcus Dicander 2005

English translation 2006-04-30
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