Explaining Gojo's Infinity with Calculus

gay akutami kind of sucks at math don't take my word for it look see he can barely count he mixed up the numbers 5 and 50 why is it then that the coolest power in jjk is super mathematical if you haven't figured it out by now I'm talking about Limitless Gojo's technique if you clicked on this video I'm sure you're familiar with it but on the off chance you aren't Limitless allows Gojo saturo to distort and manipulate space one of the uses of this makes it literally impossible to reach him but what does that mean gig explains this with the story of Achilles and the Tortoise imagine Achilles racing a tortoise but the tortoise has a head start this is one of Zeno's paradoxes who is an ancient Greek philosopher he argues that it's impossible for Achilles to reach the tortoise which sounds stupid but the reasoning is tricky first Achilles has to go halfway to the tortoise then another half of that then another half Etc in essence he has to travel halfway between him and the Tortoise an infinite amount of times so he'll never reach it but that's kind of stupid I mean think about it if that reasoning checked out then nobody nothing could ever move which to be fair is what Zeno argued motion would be impossible since you can technically subdivide any distance into Infinite Parts first of all I can move and second of all that still doesn't really explain Go's technique yes I'm overanalyzing this but just stick with me here and it'll be worth it also I have a patreon now so if you want to support me click the link in the description now believe it or not what we're debating here is something that stumped mathematicians for over 2,000 years this idea of doing an infinite number of tasks in a finite amount of time like traveling half of a distance infinite times has a name a super task actually vau did a video on these a while back now these are paradoxes but they're like incredibly impractical who cares if you tell me that motion is impossible that's not going to stop me from punching you in the face or somewhere else but believe it or not this whole idea is literally the foundation of calculus Gojo's power is literally calculus here let's take a simple example on the x- axis is how similar someone is to meami and on the y- axis the chances of being a bum a simple linear relationship I'll call it bum of X now let's say that I'm about 53% similar to Mega again I'm not proud but just looking at the graph I can pinpoint How likely I am to be a bum but there's always going to be some inaccuracy in where I put this dot now let's say I know I'm within about 5% of 53% similar to Megami again I'm not proud but then we can draw boundary lines on the X and Y axis so we know how Bumm I am lies somewhere in this rectangle okay now let's say Gojo looks at me with his six size and he can quantify that I'm exactly 53. 2 45% similar to Megami or something like that that corresponds to some bum value B I'm leaving it arbitrary for a reason now we can let the horizontal lines hone in arbitrarily close to B no matter how close they get we can always squeeze our vertical lines to hone in on 53. 2 45 in calculus what we can say is that the limit as X approaches 53.

2 45 of bum of X is B and you can write that in this compact mathematical notation we say that this is the limit because for some arbitrary margin of accuracy on the bum axis we'll call the error Epsilon I can always choose some range we'll call it Delta on the Megami axis such that the difference between our function value bum of X and our value B is within the purple lines now this whole time we've been assuming my bumpiness is always directly related to my similarity to potential man but what if we're wrong what if that's true for most points but not our point maybe that percentage corresponds to a bummin index up here then it doesn't really matter how far we zoom in these lines we'll always be wrong about my bum value the important thing to note here is that we actually don't care what value B is what value bum of 53. 2 4 5 is it could be a point anywhere along this vertical line all I care about is what value bum of X approaches as X gets arbitrarily close to 53.