Armchair Critic wrote:

"You cant start with something, add nothing, and have a total of nothing, its impossible."

In computers there are AND gates and OR gates. In an AND gate all inputs must have a signal or there is no output. In an OR gate if any input has a signal there is an output.

1 and 0 can represent a signal and no signal, respectively. If we have two signals coming in the gates the arithmetic is as follows:

OR gate

0+0=0
1+0=1
0+1=1
1+1=1

AND gate

0+0=0
1+0=0
0+1=0
1+1=1

davidf: To be fair to ArmchairCritic, you not doing arithmetic addition there, just propositional logic which happens to share the same symbols of "+", "1" and "0".

To illustrate your point better you could have asked something like this:

What does: 1 + -1 + 1 + -1 + ...(repeat forever) equal?

Does it equal 1? Since we can rewrite it: 1 + (-1 + 1) + (-1 + 1) + .... = 1 + 0 + 0 .... = 1

Or does it equal 0? Since we can rewrite it: (1+ -1) + (1+ -1) + ... = 0 + 0 + 0 + .... = 0.

Of course, a person who knows a thing or two (especially those who know about Cauchy limits and convergence) would say that I'm cheating here and are abusing the proper use of maths.

Dear david f and thinkabit,

It's good to see you using mathematics for its intended purposes: calculating and measuring.

Mathematics is a language with a great deal of internal logic- its neither a science nor a human belief system. Its totally context dependent- people who says it not just compare 10 grain of sand to 1 boulder.

I'm not ignorant.
I just know that 1+1=2.

Lets say one plus zero could equal zero.
How can you apply this miracle of backwards thinking in the real world?
What use is your madness to society?

Say I go to the bakery and buy a pie.
Then before I leave I decide maybe one might not be enough so I buy another one.
How many pies do I have?
Don't try and tell me 1, none or 3
You know what the answer is.

1+1 will ALWAYS equal 2.

Armchair Critic: As it stands, right now (today) there are no known flaws in standard arithmetic, well as far as I know anyway. By Standard arithmetic I mean arithmetic according to Peano's axioms built with ZFC set theory to make sets that form the things being talked about (whether these things be numbers, functions, operators such as addition, etc.), with first order calculus to express statements/theories about these things and some deductive system (such as a Hilbert system) to create proofs of these theories. This gobbledegook is a formal description of what you would most likely intuitively mean by arithmetic/maths.

However, just because there are no known flaws today, doesn't mean that someone won't find one tomorrow. In fact Godel's theorems guarantees that we can *never* be certain (certain within the framework of standard maths) that no flaws will ever be found.

So, to make a statement that 1+1=2 will *always* be true is to make a statement beyond/outside of maths. Ie: you are claiming something beyond which maths can prove. In other words you are relying on greater/separate power/source beyond maths to make this claim. An example of such a power is blind faith.

Now, if it is blind faith by which you make this claim, then your belief in the correctness of maths is no stronger than any other claims made on blind faith, such as those made by religious people. Note also, that I could make the counter claim that "maths is flawed" on blind faith (without a proof) and this claim would be just as valid as yours.