Poisson distribution: P[-infinity]

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I am confused with how to handle the probabilty of $P[-\infty]$

Let X be a random variable with Poisson probability distribution and $\lambda = 1.$ What is the probability $P(X>1)$?

$P(X > 1) = 1 - P(X < 1)$

$P(X < 1) = P[0] + P[1] + P[-\infty]$

$P[0] = \frac{1^{0} \times e^{-1}}{0!} = e^{-1}$

$P[1] = \frac{1^{1} \times e^{-1}}{1!} = e^{-1}$

$P[-\infty] = \frac{1^{-\infty} \times e^{-\infty}}{\infty!} = ?$