In university, if the question ask:

Prove that 1+1=2.

How to prove?

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- Jan 7th 2008, 01:59 AMSengNee1+1
In university, if the question ask:

Prove that 1+1=2.

How to prove? - Jan 7th 2008, 03:11 AMPlato
- Jan 7th 2008, 07:54 AMThePerfectHacker
- Jan 7th 2008, 08:20 AMgalactus
Having seen this before, if you were not given a set of axioms, then Peano's axioms may be helpful for this. They are:

1. Let S be a set such that for each element x of S there exists a

unique element x' of S.

2. There is an element in S, we shall call it 1, such that for every

element x of S, 1 is not equal to x'.

3. If x and y are elements of S such that x' = y', then x = y.

4. If M is any subset of S such that 1 is an element of M, and for

every element x of M, the element x' is also an element of M, then

M = S. - Jan 7th 2008, 08:36 AMJhevon
- Jan 7th 2008, 09:46 AMgalactus
The way I have seen it done is thus:

As a matter of notation, we write 1' = 2, 2' = 3, etc. We define

addition in S as follows:

$\displaystyle 1. \;\ x + 1 = x'$

$\displaystyle 2. \;\ x + y' = (x + y)'$

The element x + y is called the sum of x and y.

Now to prove that 1 + 1 = 2.

From 1: with x = 1, we see that 1 + 1 = 1' = 2.

Standard properties of addition - for example, x + y = y + x for all x

and y in S - can be proved by induction (which is based on Peano's

Postulate #4. - Jan 7th 2008, 07:52 PMmr fantastic
Alfred North Whitehead and Bertrand Russell wrote Principia Mathematica and published it in three volumes in the years 1910-1913. In it they laid the foundation of modern mathematics. On page 362, they finally got around to proving that 1 + 1 = 2.

On the other hand, 1 + 1 = 3 for 1 sufficiently large ;) - Jan 7th 2008, 07:59 PMThePerfectHacker
- Jan 7th 2008, 10:09 PMSengNee
I still confuse. Anywhere, thanks.

- Jan 7th 2008, 10:41 PMJhevon
- Jan 8th 2008, 12:37 AMSengNee
I only a student after SPM(only available in Malaysia, its standard is same as "O" level), waiting for result.

I post this because I hope to learn somethings extra. - Jan 8th 2008, 04:10 AMCaptainBlack
- Jan 8th 2008, 04:26 AMcolby2152
- Jan 8th 2008, 08:48 AMJhevon
- Jan 8th 2008, 07:48 PMSengNee
Thank you everyone.:);):D