1+1=2: Is There a Proof or Acceptance?

[FulhamFan3]

But the point still holds -- it can be done.

If you tell that person you taught to count to get 4 sticks of wood how would he actually know to get 4? They need a number to correspond to a quantity somewhere in the education. When I say teach someone to count I mean that they know the meaning of the numbers they are learning.

 

[matt grime]

Well, not really. 4 is the successor of 3, which is the successor of 2 which is the succesor of 1. I think even dictionaries define 4 as one more than 3. Perhaps you could call that the meaning of "4". Who's got the definition of definition?

Blackadder: I have two beans, and I add two more beans, what do I have?
Baldrick: A very small casserole.

 

[Hurkyl]

When I say teach someone to count I mean that they know the meaning of the numbers they are learning.

Or, are you merely teaching them the art of labelling objects with an initial segment of positive integers?

 

[VietDao29]

Hi,
I really don't think that it's worth arguing here.
We must accept that the natural numbers are: 0, 1, 2, 3, 4, 5, ...
And, if I had an honor to be the inventor of the natural number, I can make it whatever I like and my descendents just have to accept it. I can make it like:
1, 0, 5, 7, 10, 100, 20,... Or I can even create some more symbol to make different numbers.
Why 1 + 1 = 2 is you look at the array of natural number. Search where the 1 is and simply count from that number 1 more value, and you get 2.
And 2 + 3 = 5. Just do the same...
It's acceptable, and must be accepted, as you cannot do anything to change it.
It's basically correct... as I think.
Viet Dao,

 

[Alkatran]

Hi,
I really don't think that it's worth arguing here.
We must accept that the natural numbers are: 0, 1, 2, 3, 4, 5, ...
And, if I had an honor to be the inventor of the natural number, I can make it whatever I like and my descendents just have to accept it. I can make it like:
1, 0, 5, 7, 10, 100, 20,... Or I can even create some more symbol to make different numbers.
Why 1 + 1 = 2 is you look at the array of natural number. Search where the 1 is and simply count from that number 1 more value, and you get 2.
And 2 + 3 = 5. Just do the same...
It's acceptable, and must be accepted, as you cannot do anything to change it.
It's basically correct... as I think.
Viet Dao,

Are you arguing that "1" has no meaning, or that the meaning referenced by "1" cannot be defined? You seem to skip from "look I can change symbols!" to "you need '1' for '1'"

You always have to assume some rule before you can proceed in math. For example, "Math is logically consistent" is one of the main rules IMO ... Can you prove that math is logically consistent? well, it's one of the axioms, so if it isn't logically consistent it isn't math thus math is logically consistent.

Basically put: "1 + 1" can be represented the symbol we use to represent the quantity equal to "1 + 1", which is "2". Or am I being too 'superficial'?