Confusion about subtle difference between discrete-time and continuous-time In Alan Oppenheim's book Signals and Systems a comparison is made between the properties of discrete-time and continuous-time complex exponential signals in section 1.3 pg. 26.  Specifically it says: 


  The continuous-time complex exponential $e^{j\omega_0t}$ has two
  properties: 
      1.  the larger the magnitude of $\omega_0$, the higher is the rate of oscillation in the signal
      2. $e^{j\omega_0t}$ is periodic for any value of $\omega_0$
  
  Consider the discrete-time signal $e^{j(\omega_o+2\pi)n}= e^{j2\pi n}
e^{j\omega_0 n}=e^{j\omega_0 n}$. From this we see that the
  exponential at the frequency $\omega_0+2\pi$ is the same as that at
  frequency $\omega_0$.Thus we have a very different situation from the 
  continuous-time case, in which signals $e^{j\omega_ot}$ are all distinct for 
  distinct values of $\omega_0$


The part I don't understand is the one in bold . It seems to me I can do exactly the same thing for continuous-time complex exponential by replacing $n$ with $t$: 

$e^{j(\omega_o+2\pi)t}= e^{j2\pi t}e^{j\omega_0 t}=e^{j\omega_0 t}$

So there we have it.  I have produced the same signal in the continuous-time complex exponential.  So what are they talking about? I see no difference.
The problem is that $$e^{j 2 \pi t} \neq 1,$$ except in the case when $t$ is an integer. However, in that case, you have the discrete-time formula: $n$ is assumed to be an integer. In most DSP literature, wherever you see $n$ used as in this case, you can safely assume it's an integer.