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Is the exponential function even defined in the infinity point? I´ve read that it's conventionally defined equal to zero but it doesn´t make sense to me because the function is , so the limit must be the same for every path, therefore if the limit would be actually zero, when I approach for the real axis the limit would be $\infty \ne 0$, which is an absurd.

Panchito
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  • Related https://math.stackexchange.com/questions/2212798/complex-limit-of-an-exponential – Joe Jul 12 '21 at 01:54
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    Limits don’t care if the function is defined there. The corrrect question is whether there is any possible value at $\infty$ which we can define there and keep it continuous. – Thomas Andrews Jul 12 '21 at 02:13
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    Where did you see it defined as $0?$ The only place where that might be true is at $-\infty$ on the extended real line, but that is not the same as $\infty$ on the complex numbers. – Thomas Andrews Jul 12 '21 at 02:17

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