@sungod9797
We can prove using basic Diff Eq that an object approaching Gojo can never reach him if it slows down proportionally to the remaining distance left as a fraction of some initial distance from Gojo. The problem could be expressed as a simple ordinary differential equation of the form y’ = v*(p-y)/p, where y(t) is the position (distance traveled to Gojo), p is the initial distance from Gojo, v is the initial velocity, and y’(t) is obviously the current velocity. By separation of variables, this becomes (1/(y-p))dy = (-v/p)dt -> ln|y-p| = -tv/p + C -> y = p + Ce^(-tv/p). At time 0, y = 0, so C = -p. So, y(t) = p(1-e^(-tv/p)). Finally, we try to find the amount of time it takes for the right hand side to equal p (when all the distance is covered). This occurs when e^(-tv/p) = 0. But this never occurs for any value of t, even though the value of the expression exponentially decays towards zero as t goes to infinity. Thus, at no time will the object reach Gojo. Probably an unnecessary amount of work, but still kinda fun to show with a basic ODE lol The interesting thing is that in the anime, the technique seems to be visually depicted more like a barrier than can actually exert force to push you away from Gojo (without using red), as shown when he crushes Hanami against the wall, or when the knives suspended in mid-air move away from him as he walks forward.
@Plupert
When I watched JJK and Gojo was showing that Jogo would never be able to touch him but he never actually “stopped” moving towards him. My immediate thought was oh Gojo is like an asymptote. I’m happy someone else thinks like I do.
@chlorine-17
I actually had this same realization a while ago, and it also kind of works for his extension techniques too. While blue seems to hinge more on the fact that it’s introducing a negative number into reality, I see it as a point approaching negative infinity which causes it to constantly draw in the space around it. Then red would be causing whatever’s in front of it to “approach positive infinity” by being blasted away, and purple makes a point that approaches positive infinity from one side and negative infinity from the other, so the limit (and thus everything in the purple) does not exist.
@Fotoschiki
I had divergence, convergence and the definition of infinity in my first semester studying electrical engineering, while I watched JJK season 1. It was litterally in the same week our professor first used these words when Gojo explained his powers. It still feels surreal.
@CamiWuzHere
seeing the megumi graph and watching him get roasted for like 5 minutes straight hurt my heart😭😭
@GokuEnjoyer69
In JoJo part 6 there’s a really similar concept which makes much more sense to how Gege explains infinity. Every time someone reaches halfway to Dio’s kid, they shrink to half their size, making the distance to travel to the next halfway point the same every time.
@SparkyMasterK
at 7:31 When you brought up the infinity barrier line I thought for sure you were going to say "this is a piecewise equation so at that x-value the function changes has two different domains, Hence why they say 'Domain expansions" Literally the moment they change reality.
@tiringking
The moment the graph of megumi showed up I was praying for a bum reference. I was not disappointed.
@udiomoudochi8696
This man did not fail to call Megumi a bum any opportunity he got.
@gunther268
Bro mahoraga so smart it mastered calculus and mathematics in a matter of 10 spins 🤯🤯
@xendurr8180
Gojo is such a good teacher that even in the end he still manages to teach us how to do fractions.
@degen7278
And here I scoffed at my teachers telling me id use calculus. Dont I look silly now.
@picklesbigpp897
I like the fact that i was trying to find a vid on calculus so i can do my math homework but get this instead but it does the job
@user-11Il10I1
Potential man catching stray is crazy 💀
@Galactic1078_
I have been learning this at school the past year, why did I understand this better than my teachers lessons
@HENRIQUEKOUTAROSAGAHARA
Broo no way. Youtube blessed me with this piece of art.
@Yittery
MORE VIDS LIKE THIS PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE THIS IS SO GOOD
@daegukreb4219
man, this really just reminds me of the two all nighters spent on the math IA -- you expressed it so concisely and in much simpler terms compared to my calc knowledge at the time.
@ethanramos5372
I’m glad you made this video. I happened to be taking calculus when jjk was first coming out and we were literally learning limits, asymptotes, all that. I made the connection that gojos ability is literally that.
@ChucklinHSR