Yep. ∞ is infinitely big in the same way that 0 is infinitely small. -0 = 0 and -∞ = ∞. Opposite ends of the circle. (Or the Riemann sphere if you like complex numbers.)
While this Riemann sphere seems like a useful concept, -∞ = ∞ is an observation that doesn’t seem to hold true outside this spherical model of complex numbers. Just add ∞ to the both sides, and you end up with 0 = ∞ + ∞ which is most certainly not true.
Pssh, I’ll divide by zero all day. You just need -infinity=infinity (think a number circle instead of a number line), and you’re good.
It’s 0/0 where the real crimes begin.
Use L’Hôpital. Manual in Russian.
For an easy approximation by this rule, just differentiate both numerator and denominator by the same variable and apply the limits again.
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Yep. ∞ is infinitely big in the same way that 0 is infinitely small. -0 = 0 and -∞ = ∞. Opposite ends of the circle. (Or the Riemann sphere if you like complex numbers.)
While this Riemann sphere seems like a useful concept, -∞ = ∞ is an observation that doesn’t seem to hold true outside this spherical model of complex numbers. Just add ∞ to the both sides, and you end up with 0 = ∞ + ∞ which is most certainly not true.