this post was submitted on 16 Nov 2023
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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.
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.
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.
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 ∞ + ∞ = ∞