Mathematical question

[Yanagi]

Hi,

Can anyone in here give me mathematical proof that 1+1 = 2?

Cheers

 

[TuxDave]

I would never have figured this out by myself.

 

[GoHAnSoN]

1/2 + 1/2 = 2/2
1*2 + 1*2 = 2*2

so 1+1 = 2

 

[Matthew Daws]

The issue here is that what do you mean by the symbols "1", "+" and "2"? Once you've defined them, a "proof" that 1+1=2 is almost completely trivial (because 2 is pretty much DEFINED to be 1+1).

--Matt

 

[f95toli]

It is not as trivial as that, look for example at the page TuxDave linked to.
There is also a longer proof which does not use all the axioms (of course it uses some). I think it first appeared in Principia Mathematica (the book by Russel&Whitehead published around 1900, has nothing to do with Newton). I have seen it but I don't remember where.

 

[silverpig]

Yeah, I took a philosophy of logic class where the real number line was constructed like that. It's pretty weird to think of it that way. I've also seen derivations like so:

0 = {} (the number of elements in the empty set
1 = {0} (the number of elements in the set containing zero
2 = {0,1}
3 = {0,1,2}

etc.

 

[Gen Stonewall]

Proofs exist to show that a postulate holds true in all cases where it claims to hold true. It seems perfectly satisfying to verify the value of 2 simply through its definition. Do the minimum amount of work that will get the job done!

 

[Kibbo]

Originally posted by: Gen Stonewall
Proofs exist to show that a postulate holds true in all cases where it claims to hold true. It seems perfectly satisfying to verify the value of 2 simply through its definition. Do the minimum amount of work that will get the job done!

That seems tautological to me. But I may be wrong. I like they linky more.

Does anyone on here know that mock-proof that 1+1=3?

 

[Machupo]

or the mock proof that says 1 = -1

 

[TuxDave]

Originally posted by: Gen Stonewall
Proofs exist to show that a postulate holds true in all cases where it claims to hold true. It seems perfectly satisfying to verify the value of 2 simply through its definition. Do the minimum amount of work that will get the job done!

But 2 is not defined as 1+1. It is defined as the successor to 1 in the natural number system. Addition needs to be defined before proving 1+1=2

 

[bendixG15]

Like so many "mathematical problems"
this one has nothing to do with mathematics.
Its symantics...playing with the meaning of words....

If you can't "prove" that 1+1=2
then
can you prove that 1+1=/2 (does not equal 2)

Can you prove that "zero" exists ??