C Why Am I Getting A Run-time Error For These 2 For Loops

Pretty major string error: C++ help (for / string help)?

I have no idea what is wrong with the following code (if you ignore vs 2010's bitching about it blowing up) it outputs exactly what I want.

The following is the output I am hoping to achieve:
1
12
123
1234
12345
12345
1234
123
12
1

____________________________

The code that I am using to do this is 2-nested for loops:

#include
#include
#include

using namespace std;


int main()
{
int i=0, j=0;
string a("12345");
for (i=0; i<=5; i++ ){
for (j=0; j<=i; j++){
cout << a[j];
}
cout << endl;
}

for (i=5; i >= 0; i-- ){
for (j=0; j<=i; j++){
cout << a[j];
}
cout << endl;
}
return 0;
}

______________________________________...

The output works perfectly, however vs2010 pro pops up with the following error every time I compile it:

"Debug Assertion Failed!

program (program name here)
File: c:\program files (x86)\microsoft visual studio 10.0\vc\include\xstring
Line:1441

Expression: string subscript out of range

For information on how your program can cause an assertion failsure, see the VC++ documentation on asserts.

(press retry to debug the application)

Abort / retry / ignore.


If I ignore twice the output comes out fine.... what is happening here?

How do I get rid of this error message on Windows?

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What are the differences between syntax, run time and logic errors.?

1) Syntax Errors are errors in the syntax of your code. This kind of error is the easiest to figure out. They are revealed when you attempt to compile your program. An example would be as mentioned above; forgetting the semi colon at the end of a statement in a language like C#

2) Run time errors are unhandled errors that are raised during runtime. For example, your code fails to get access to a remote machine. There is no way to be sure at compile time (when you compile your program) whether this error is SURELY going to happen or not. You can suspect that it happens though.

3) Logic Errors are the sneakiest. Your syntax is correct. No runtime error is being raised, however your program logic is not correct (for example an incorrect formula).

Hope the above helps