9 with the aid of fact if a cases or divide is in a question with a upload or subtract then the guideline is you do this first then upload the addition/subtraction. The brackets point out that that component of the equation desires to be performed one after the different an then extra decrease back to the equation. with the aid of fact there is not any longer image earlier the brackets and the the branch is next to the equation you may then cases the two ultimate numbers jointly to get 9. So: 6/2 = 3 x (one million+2) =3 x 3 = 9
Well....that depends on WHAT you are adding and HOW.... instead of using 2+2 lets make it simpler and use 1+1....
1 liter alcohol + 1 liter of water DOES NOT = 2 liters of solution ;-)
And thats a FACT im not making it up....addition is very subtle and actually depends on several factors....
consider the following example:
1+1=2?
let a=b
a^2=ab
a^2+a^2=a^2 + ab
2a^2=a^2 + ab
2a^2-2ab=a^2+ab-2ab
2a^2-2ab=a^2-ab
2(a^2-ab)=1(a^2-ab)
2=1
then 2+2=2 or 2+2=1 or 1+1=1 and finally 1+1=2
consider a+b=p where a,b,p>0
then...
d|a+b=d|p where d=1 and p is prime
then...
p|a and p|b for a,b >= p
In a commutative ring (R,+) the OPERATION (a) + (b) of two principal ideals is itself a principal ideal (d) if and only if (d) is a greatest common denominator of (a) and (b)
The ideals in a ring (R,+) form a lattice under ordinary inclusion relation with join given by (a) + (b) and meet by the intersection B in C.
If integers m & n have (d) as a greatest common denominator then the ideal SUM (a) + (b) is principal ideal (d)
(d) <-U (a) and (d) <-U (b) since (d) = rb+sc any ideal containing a and b must also contain d so all (d)
Therefore..... (d) = (a)+(b)....so THIS IS WHY 1+1=2 and 2+2=4 and not the other possible answers (isnt 2 a gcd of 4, see the point?)
Well this problem is as much philosophical as it is mathematical.
The easiest (and somehow least satisfying) way to answer you is to say
that it is definitional that 1+1 = 2 and that n + 1 = the next number bigger
than n.
So 2+2 is 2+1+1, which is 3+1, which is 4. The other way to think about it
is that + signifies the combining of two quantities, and the name for the
quantity that is the same size as 2 combined with itself is 4.
It really does come down to the "fact" that that is the definition.