Is it possible to have a situation where A + B = B?

Question

This seems like a mathematical impossibility, but I'm guessing there will be a numbers genius out there who will show how it is possible.

Answer 1

If A and B are members of a group under the operation +, then by definition, there will always be an identity element, I, in that group with the property I + A = A = A + I for every element of the group.

The integers, rational numbers, real numbers, and complex numbers are all groups under addition, so they all have an identity member, namely 0.

Vector spaces are also groups under addition as are matrices (a subset of vector spaces) so they also have additive identities -- the zero vector and the zero matrix.

Answer 2

A=0

Answer 3

A=0 B=4
a+b=4

Answer 4

If A=0, then A + B = B.

Answer 5

this statement will only be true if A = 0, and there are some possibilities for a to be zero :

the first, A = cos 90 degree or sin 180 degree

or, A = 1/infinity

and B is B

Answer 6

Only A=0 would work. If this happpend though it would just be easier to say B. To get other possibilities for A instead of 0, you would need variables like 6 + -2 (4)=-2.

Answer 7

If A == 0 then A + B == 0 + B == B.
If B == infinity then A + B == A + infinity == infinity == B.
Otherwise, we're talking about higher level
math concepts like vectors, matrices, and additive identities.

Answer 8

If A = 0 then A + B would still be equal to B; other than that i cannot see how it is possible.

Answer 9

If A=0, then whatever B=, A+B will always =0

Answer 10

Not an impossibility at all. If A = 0, your equation will be true.