I think the point here is “Why simulate when you can get an exact answer?” In which case, the consideration is whether it is easier to ‘see’ that the simulation program is correct or that the reasoning for the exact answer is correct.
A similar situation that comes to mind is “exact” symbolic integration vs. “approximate” numerical integration; symbolic integration is not always possible (in terms of “simple” operations) whereas numeric integration is straightforward to perform, no matter how complex the original formula, but inexact.
Yes—while reasoning through the problem might give you a deeper understanding, if you just want to know the answer it can sometimes be easier to be sure that your program is correct than that your mathematical reasoning is correct.
I think the point here is “Why simulate when you can get an exact answer?” In which case, the consideration is whether it is easier to ‘see’ that the simulation program is correct or that the reasoning for the exact answer is correct.
A similar situation that comes to mind is “exact” symbolic integration vs. “approximate” numerical integration; symbolic integration is not always possible (in terms of “simple” operations) whereas numeric integration is straightforward to perform, no matter how complex the original formula, but inexact.
∫(0 to 7) 5 dx ≈ 35.000
Yes—while reasoning through the problem might give you a deeper understanding, if you just want to know the answer it can sometimes be easier to be sure that your program is correct than that your mathematical reasoning is correct.