$\infty$ sometimes means "a very big positive number" (with $-\infty$ taking on the meaning "a very big negative number"). To state the matter intuitively, no matter how many times you add $0$ to $0$, even infinitely many, there's no reason to think the propensity for reaching a larger value is greater than the propensity for reaching a smaller value. This is due to the fact that the mapping $\mathbb = -\infty.$$
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