this post was submitted on 07 Jul 2023
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Showerthoughts
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Thats incorrect too, the real answer is that its undefined. Infinity only is the correct answer if you only examine it from the positive side, so limit of a/x as x goes to 0 is infinity, but if x starts out as negative, the answer would be negative infitnity, causing a logical paradox.
Notice I never said the value IS infinity. I said it “goes to infinity” which is the mathematically correct way to describe what’s going on when considering the limit, at least on the positive side. Of course, because on the negative side of zero, the function goes to negative infinity, it makes the most sense to describe it as undefined, still. 😉
https://upload.wikimedia.org/wikipedia/commons/thumb/4/43/Hyperbola_one_over_x.svg/800px-Hyperbola_one_over_x.svg.png