I'm pretty sure that it's fine, if the rates are understood to be per year (or some other finite period), as is usually the case in economics.  After a year in the bank, an amount of money M becomes M*(1+i), where i is the nominal interest rate.  You can also write this as M*(1+r)*(1+p), where r is the real interest rate and p is the rate of inflation.  Then you get the first equality for r.  It reduces to i - p when p is small, or if the rates are measured instantaneously (something that probably only a mathematicians would do). -