I wouldn’t trust that article on iOS 15 jailbreaks. A lot of those is misleading/fake (e.g. Checkra1n only supports iOS 12-14, unc0ver does not support iOS 15 and unc0ver virtual doesn’t exist).
iOS 15 currently only has Dopamine and Palera1n as supported and recommended jailbreaks. Though if you only need to side load apps, take a look at TrollStore, which lets you side load apps indefinitely, but isn’t a full jailbreak (made by the same dev as Dopamine).
FYI Checkra1n isn’t that old, but there are a lot of jailbreaks that end in “ra1n” :)
There are lots of applications, so I’ll give you three
Factorials are used in the Taylor Series to approximate trigonometric (sine, cosine, etc) and the exponential function. This can help speed up calculations.
In probability and statistics, if you want to find how many different ways a deck of cards can be shuffled, the answer is 52! Because the first card can be any of the 52, the second can be any of the remaining 51, and so on until the last card. Building upon this concept results in ways to model data like the binomial distribution , which is simply “how many successes will i get if i do this trial a certain number of times”. E.g. If I flip a coin 100 times, how many times will it be heads?
In computer science, the complexity of a program is compared to functions like the factorial, exponential, quadratic, etc. to visualize it’s performance given the size of the input, n. E.g. a program of linear time complexity is denoted as O(n), and as n increases, we expect the time for the program to finish to increase linearly. For a factorial time complexity, O(n!), we expect the time to complete to increase a lot compared to O(n)