How can you prove that 2+2=4?

Answer 1

There is no way to prove it because math cannot be proven.

Answer 2

We start with the number zero, which can, for example, be defined as the empty set. Now we define, for each number n, a successor s(n), for example by
s(n)= {n}

We can now give names to the numbers:
1=s(0)
2=s(1)
3=s(2)
4=s(3)

We now define the "+" operator, starting with the definition
n+1=s(n)
and, further,
n+s(a)=s(n+a)

setting a=1 and n=2 we have
2+2
=2+s(1)
=s(2+1)
=s(s(2))
=s(3)
=4

As you see it takes a lot of definitions and very little reasoning. So you could say that it's hardly interesting. However, it helps to illustrate how many things you have to define. And maybe it makes you wonder how different math could look like if the definitions were chosen otherwise.

More importantly, you may wonder, for each of the many definitions, if they are actually meaningful. It could be, for example, that the numbers where cyclical: suppose
s(7)=0
then there would only be eight numbers. This is not the case, as you know: there are in fact an infinity of numbers, which is related to the fact that there's NO n for which s(n)=0. Unless you augment the numbers with negative numbers, of course. But they don't exist in the (limited) system I proposed: since everything can ultimately be reached by starting with zero and adding up, all number are positive.

Lot's of food for thought. Elementary math is the math I like best.

Answer 3

First you need to define that 1 exists.

Then you define that for every element, a, that exists, there is a successor a + 1. Note that the "+" is the simple addition operation.

We define 2, 3, 4 as follows:

Given that 1 exists and that it has a successor 1+1 = 2,

Since 2 exists, it has a successor 2+1 = 3,

and since 3 exists, it has a successor 3+1 = 4.

So, we have ((1+1)+1)+1 = 4

Since addition is associative, (a+b)+c = a+(b+c), we rearrange the brackets,

((1+1)+1)+1 = 4

(2+1)+1 = 4

2+(1+1) = 4

2 + 2 = 4

Solely based on the definitions above.

Answer 4

I would have to sugguest a proof by contradiction:

1) Start by assuming the opposite of our statement to be true (i.e. that 2+2 does not equal 4)
2) Now, add 2+2 resulting in 4
3) Thus we have 2+2=4 which is a contradiction to our begining assumption.

Thus, since it is false that 2+2 does not equal 4, then 2+2=4.

That's my best stab at making a mathematical proof for such a trivial question.

Answer 5

4 - 2 = 2

Answer 6

If we use transposition, like in algebra we transpose 4 to the other side thus we get 2+2-4=0 then 2+2 is 4... Then we get 4-4=0 then 4-4=0 then we get the equation 0=0 which is true. Its just as simple as that....

Answer 7

do u know couting
u have 2 oranges with u
and 2 with me
i give u the two to u so now u have 4 oranges with u
yeh i proved it
give me my points

Answer 8

Because on paper with the number system it looks like something that can simply be disproved but in real life if you take two objects and add them to two other objects you get four objects:

II + II = IIII

Math is just a written way of explaining the physical world around.

Answer 9

2 and 2 add up to four by definition because the second number in the series of positive integers is ascribed the name two and the fourth number is ascribed the name four.

i.e. it is an axiom of the number system that the second number plus the second number equals the fourth number, whatever the names and symbols we ascribe to them and whatever number base we are in.

e.g. we could call the second number deux and the fourth number quatre and then it would follow that deux and deux = quatre.

Answer 10

to prove 2+2=4 is possible
if we are taking two pen in our one hand and two other pen in our next hand and count it in total you will get it as 4 in total