Supertasks

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Recommends Victor Palea · 2020-05 · Mathematics Stack Exchange · on “Intuition behind Heine definition of the limit of a function”

If you are allowed to use the limit to formulate the limit of a sequence, I guess you could also use it instead of the $\epsilon$ formulation. As for the natural interpretation, try Vsauce on Supertasks [this video] . Although it might not be good as a material for students (since Michael jumps from one thing to another as he does), I think that you might find some scenarios there that should be puzzling at first sight, but can be used to showcase the meaning of a limit. Once you have that solved try to apply it to the limit of a function. One example that comes to my mind is as follows: Suppose you are on a mountain and you want to get to the peak. We assume that I can climb to the peak however

Cites Zach Barham · 2013-10 · Mathematics Stack Exchange · on “Counting down by halving to 0”

Say that you are counting down from 10. You say how long is left after half the amount of time you said how long was left (Like 10, 5, 2.5, 1.25, 0.125, etc.). Because when you halve repeatedly you can never get down to 0, wouldn't you have to say how long is left infinitely many times before you can reach 0 seconds? Update: 8 months ago, Vsauce uploaded a video about a similar problem to this, which he called Supertasks : Watch it at [this video] .

Cites Theraot · 2018-03 · Mathematics Stack Exchange · on “The "Paradox" of Hilbert's Hotel”

I believe this is more of an issue of the particular language used here, and not so much of the math. With that idea in mind, I will try to walk you over this as carefully as I can. Without any loss of the mathematical understanding. Imagine a Grand Hotel with a (countably) infinite number of floors and rooms. Here, countably refers to a particular kind of infinity. However, the term "countable" can be confusing misinterpreted if you are not familiar with the term. As, you see... "countable" does not mean that you can count the rooms as a real thing that can happen in the real world (that would be a supertask [this video] ). Instead it means that it is the kind of infinity that corresponds to the

Cites Tessa Painter · 2022-06 · Mathematics Stack Exchange · on “If you're watching a live stream and n number of minutes behind the live feed, how much time would it take while watching at s speed to catch up?”

Sometimes I'll tune into YouTube livestreams a few minutes late, but I want to watch the whole thing and catch up with the live feed, so I'll start from the beginning at 2x speed or 1x speed. I'd like to find a way to calculate exactly how much time it will take for me to reach the live feed. So if I start watching 20 minutes behind at 2x speed, after 20 minutes of watching, I'll be 10 minutes behind, after 10 minutes, I'll be 5, etc. I would guess this would look something like this $ total = \frac{20}{2} + \frac{10}{2} + \frac{5}{2} + ... $ How would you create a general equation for this? Could you use summation, product, or something like a Taylor series? I recall an old VSauce Video [VI