/sci/ - Science & Math

I highly doubt that pic related is a valid proof that exp(z+w) = exp(z)*exp(w). I understand that zw/n approaches 0, but limits usually don't work that way, do they? Because following this way of thinking, the whole fraction (z+w+zw/n)/n would approach 0 and the whole thing would be equal to exp(1). So is this proof wrong or am i missing something?