Prove that 1+1=2?

Answer 1

check Dr. Math

http://mathforum.org/library/drmath/view/51551.html

=)

Answer 2

a calculator,
a visual (one apple and another apple, 2 apples)
what is it geometry? lol.

Actually, I found this, the link is below:

"Date: 06/10/99 at 10:15:58
From: Doctor Rob
Subject: Re: Need the math proof for 1 + 1 = 2

The proof starts from the Peano Postulates, which define the natural
numbers N. N is the smallest set satisfying these postulates:

P1. 1 is in N.
P2. If x is in N, then its "successor" x' is in N.
P3. There is no x such that x' = 1.
P4. If x isn't 1, then there is a y in N such that y' = x.
P5. If S is a subset of N, 1 is in S, and the implication
(x in S => x' in S) holds, then S = N.

Then you have to define addition recursively:
Def: Let a and b be in N. If b = 1, then define a + b = a'
(using P1 and P2). If b isn't 1, then let c' = b, with c in N
(using P4), and define a + b = (a + c)'.

Then you have to define 2:
Def: 2 = 1'

2 is in N by P1, P2, and the definition of 2.

Theorem: 1 + 1 = 2

Proof: Use the first part of the definition of + with a = b = 1.
Then 1 + 1 = 1' = 2 Q.E.D.

Note: There is an alternate formulation of the Peano Postulates which
replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the
definition of addition to this:
Def: Let a and b be in N. If b = 0, then define a + b = a.
If b isn't 0, then let c' = b, with c in N, and define
a + b = (a + c)'.

You also have to define 1 = 0', and 2 = 1'. Then the proof of the
Theorem above is a little different:

Proof: Use the second part of the definition of + first:
1 + 1 = (1 + 0)'
Now use the first part of the definition of + on the sum in
parentheses: 1 + 1 = (1)' = 1' = 2 Q.E.D."

Answer 3

Who said 1+1 =2

1+1 may be 2, but 1 + 1 can be equal to 10 too (You did not mention the base, think in base 2). I kidded son, its just an axiom. There are 8 axioms like this in mathematics where you have to accept it if you want to live in this world, for your info, here it is...

1) if 'a' and 'b' are integers then 'a+b' is an integer and 'a.b' is an integer (Closure law)
2) a + b = b + a and a..b = b.a (cumulative law)
3) a + (b + c) = (a + b) + c (Associative law)
4) a (b + c) = a.b + a.c (Distributive law)
5) a + 0 = a = 0 + a (Additive Identity)
6) a.1 = a = 1.a (Multiplicitive Identity)
7) for all integer 'a' there is a unique integer (-a) such that a + (-a) = 0
8) I can't remember...

Answer 4

It's not a matter of proof or evidence, it's what is deemed by society to what the actual answer is. As far as we know, yes one (1) plus (+) one (1) equals (=) two (2), but why? Why must those two numbers equal to that of in this case two? Society tells us that when we for example look at our fingers, which we are told we have five (5) on each hand, and count one finger, meaning an individual finger not equal to the rest that is ONE (1) finger, thus when you add another individual finger separate from all the other fingers, you have TWO (2) fingers. But then again, society grants what is mathematically correct and what isn't. As far as we know, what we see at 1 + 1 equalling 2, is in reality 3 or 4, but it all depends on what not as a governmental society has told us, but as a individual, existential, mental society has told us.

Just like in "1984" by George Orwell, "Freedom is the freedom to say two plus two make four. If that is granted, all else follows". But in the end, society tells the protagonist 2 + 2 = 5, and he agress. So it's in the eye of the beholder.

Your question should not belong to the Mathematics section, but in the "philosophy" section, but I appreciate it otherwise.

Feel free to respond, and seeing that most of the people here at Yahoo!Answers are thoughtless peons, I know I shall be ridiculed for this "answer", but in all actuality, I could care less.

Sorry if this wasn't in the "form" of an answer.

Answer 5

OK, I've done this for 2+2=4... Here goes for the simpler one...

First, we need to define the basic terms with which we will be working.

Let 1, the symbol for the unit, be taken as an axiom.

Define the operation "+ 1" as being "Move to the successor of 1"

Next, name the successor of 1: it is, in English, named 2.

With that, we can now procede to the proof, simple though it is...

Thus, 1 + 1 = successor-of-one = 2

Believe it or not, in an advanced math course (Real Analysis), we started with the simple concept of one, and of successorness, and had to build all of mathematics. Took us about a semester to get to simple, one-variable calculus... This proof was actually about day one of the class...

OK, I'm a math freak.

Answer 6

well since 2+2=4 (/2)
so 1+1=2... !!!

Answer 7

1+1=2 .. thats right unless you are thinking 1+1=11

Answer 8

1+1=2 thats all you need to know.

Answer 9

Its not, its 11

Answer 10

Drop a ball in a box (1). Now drop another ball in the box (1). Now, how many balls are in the box?

Is this really hard for you? If so-- algebra's gonna kick your a$$.