Why am I getting multiple definition error when header included? - c++

Question

I declare a Algebra.h file which holds the declaration of an add() function:
#ifndef Algebra_
#define Algebra_
namespace Algebra{
int add(int x, int y);
}
#endif
Then I implement add() as:
Algebra.cpp
#include "Algebra.h"
namespace Algebra{
int add(int x, int y){
return x+y;
}
}
Then I have classes A and B, which include Algebra.h:
B.h
#ifndef B_
#define B_
#include "Algebra.h"
#include <iostream>
class B{
public:
void func(int x, int y);
};
#endif
B.cpp
#include "B.h"
void B::func(int x, int y){
int val = Algebra::add(x,y);
std::cout << "B : "<< val << std::endl;
}
A.h
#ifndef A_
#define A_
#include <iostream>
#include "Algebra.h"
#include "B.h"
class A{
public:
void func(int x, int y);
};
#endif
A.cpp
#include "A.h"
void A::func(int x, int y){
int val = Algebra::add(x,y);
std::cout << "A : " << val << std::endl;
}
main.cpp
#include "A.h"
#include "B.h"
#include "Algebra.h"
int main(){
A a;
B b;
a.func(3,4);
b.func(3,4);
int val = Algebra::add(3,4);
std::cout << "main : " << val << std::endl;
}
I tried compilation using
g++ A.cpp B.cpp main.cpp -o bin
g++ A.cpp B.cpp Algebra.cpp main.cpp -o bin
I get this error:
/tmp/ccBXhev4.o: In function 'Algebra::add(int, int)':
main.cpp:(.text+0x0): multiple definition of 'Algebra::add(int, int)'
/tmp/ccfaCF5H.o:A.cpp:(.text+0x0): first defined here collect2: error:
ld returned 1 exit status
I even tried inlining the add() function in Algebra, but still get the error. Also I don't want to make Algebra be a class.
Why am I getting a multiple definition error even though I am adding the Algebra header file, and it does not define but only declare?