Proving 1+1=2 - Mathematically Explained

[Delzac]

Hi all,

My teacher once told me that 1+1=2 is provable, mathematically. True enough it can be done after i google it, but why is there a need to prove it so tediously, i can do it with my fingers. :)

Delzac

 

[Checkfate]

I am not 100% sure but I am pretty sure that it will have something to do with the definition of the real number system and real numbers etc.

 

[HallsofIvy]

Actually, it goes back to the construction of the "counting numbers" themselves.

Why is there a need to prove it? Well, no need at all for the average person. It is most often done as a simple exercise in the use of Peano's axioms for the counting numbers.

 

[DaveC426913]

Hi all,

My teacher once told me that 1+1=2 is provable, mathematically. True enough it can be done after i google it, but why is there a need to prove it so tediously, i can do it with my fingers. :)

Delzac

I'm going to assume that, since you're posting this, you do seriously want an answer.


Consider: when you do it on your fingers, how do you know it's true? Other than because someone, somewhere has told you "it just is, trust me".

 

[StatusX]

The difficult part is defining 1 and 2. Once this is done, the proof is almost trivial. Usually this is done using peano's axioms, but this is just one way.

 

[Delzac]

what do you mean whether 1+1 =2 is true? ( how can is not be true?)

 

[Delzac]

just to add on, say we define 1 as one unit of something

the 1 + 1 = two unit of somthing = 2

Unless you let 3 become two unit of something. then 1+1=3