General question about renaming variables

Oneiromancy

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Sep 28, 2007
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Solving a simple differential equation like dy/dt + (2ty) = 0, we end up with y = e^(-t^2) * e^c. If we rename e^c = A, wouldn't A only have the range of values A > 0? My book keeps saying "A can be negative, 0, or positive."
 
A can be positive or negative, but in the real numbers e to the 'anything' is never 0.

Unless we want to count negative infinity/complex realm

Then, \(\displaystyle e^{{-\infty}+2C{\pi}i}=0\)
 
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