Question

Why is 2 + 2 equal to 4, and not 5?

Answer 1

i wondered that myself

Answer 2

good question

Answer 3

Because he or she did a right answer.

Answer 4

it is five if the are error presents during the calculation.

Answer 5

It's a good question...but to answer and to understand it's answer a good amount of knowledge is required

Answer 6

Alright,try to understand what exactly is 2,it's not a thing that we can buy,like you can't buy 2 but you can buy 2 eggs.So 2,3 and 4 are just concepts for understanding and qualifying things,We define then natural numbers as 1,2,3,4,5,6,... to infinity the sequence increases in airthmetic progression with the common difference 1, so when you are saying 2+2 you mean to go 2 distance from 2 which in this case means 2+1+1 now what is the fourth natural number?

Answer 7

Albeit,2+2=5 has got some other significance please read here : http://en.wikipedia.org/wiki/2_%2B_2_%3D_5

Answer 8

2+2=5 (for large values of 2)

Answer 9

@UnkleRhaukus:How large ? :P

Answer 10

to 1 significant figure
2.4999... ~ 2

Answer 11

bcoz 5+5=10 and not 11

Answer 12

bcz 4 is jus wat we call dat number ...suppose u calculate 2 nd 2 on ur finger...u end up wid 4 fingers....meaning....on adding u get 4..

Answer 13

FoolForMath is no fool in math.

The deep logic here is complicated, but the best way to way to think about this is just in simple terms:
A. 2 is defined to be 1 + 1
B. 3 is defined to be 2 + 1
C. 4 is defined to be 3 + 1
D. 5 is defined to be 4 + 1

Using these definitions of what 2, 3 and 4 mean, and the axiom of the associative property of addition (call that P): then

2 + 2 = 2 + (1 + 1), by A, the definition of 2
= (2 + 1) + 1, by P, the associative property of addition
= 3 + 1, by B, the definition of 3
= 4, by C, the definition of 4

Now we could have defined the symbol & to be 3 + 1; the choice of the symbol "4" is arbitrary and convention. We could say that integers don't have associate property of addition and then we wouldn't be able to show that 2 + 2 = 4. 2 + 2 would be some other formal construction, call it # say, and we couldn't say much about the relation between # and 4.

But like all other logical analyses and systems, we have to start with some basic definitions and axioms. If you don't want to accept them and construct your own logical system with a different set, you're obviously welcome to do so.

But the definitions and the associate axiom I've used above are the things we usually assume and having made that assumption, then indeed 2 + 2 = 4.

Now why is 2 + 2 does not equal 5. Well suppose 2 + 2 did equal 5. Then 4 = 5. But 5 = 4 + 1.

If we now add other usual axioms for integers (the existence of the additive inverse; the existence of a zero 0 with the property that 0 + n = n; the commutative property of addition) we can show that
5 = 4 + 1
implies that
0 = 1.

We also usually include in our axioms the existence of a number 1 such that 1.n = n for all n and that 1 is not equal to 0.

Hence if we also make this assumption it can't be that 1 = 0 and therefore 5 is not equal to 4 and therefore 2 + 2 is not equal to 5.

Again, you might say "I don't want those assumptions". Fine, make your own arithmetic and algebraic structure without them.
But these are the usual axioms we start with and if we do, we obtain the result that
\[2 + 2 = 4 \]
and
\[2 + 2 \neq 5\]