this post was submitted on 16 Nov 2023
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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.
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.
This is only true if both infinite are the same, but one is negative. As a general statement you're right, that this is not true.
Well - in the post I replied to there was explicit talk about +∞ and -∞, upon which I believe it is fair to say that ∞ is positive in this example.
That's why ∞ - ∞ is left undefined (same as 0/0 and ∞/∞)
adding ∞ to both sides does not create a ∞ - ∞ situation, though. The substraction is a whole different topic, because it becomes an elimination problem, whereas ∞ + ∞ = ∞
Sure. And it also doesn't help to avoid the problems with division by zero. But lucky we're posting in the shitpost section, so we don't have to worry too much about details.
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.