Anti-Piracy Ad by The IT Crowd (2007)
Source. The fundamental concept of calculus!
The reason why the epsilon delta definition is so venerated is that it fits directly into well known methods of the formalization of mathematics, making the notion completely precise.
Generalize function to allow adding some useful things which people wanted to be classical functions but which are not,
It therefore requires you to redefine and reprove all of calculus.
For this reason, most people are tempted to assume that all the hand wavy intuitive arguments undergrad teachers give are true and just move on with life. And they generally are.
One notable example where distributions pop up are the eigenvectors of the position operator in quantum mechanics, which are given by Dirac delta functions, which is most commonly rigorously defined in terms of distribution.
Distributions are also defined in a way that allows you to do calculus on them. Notably, you can define a derivative, and the derivative of the Heaviside step function is the Dirac delta function.
The best example to look at first is the penalty kick left right Nash equilibrium.
Then, a much more interesting example is choosing a deck of a TCG competition: Magic: The Gathering meta-based deck choice is a bimatrix game, which is the exact same, but each player has N choices rather than 2.
The next case that should be analyzed is the prisoner's dilemma.
The key idea is that:
- imagine that the game will be played many times between two players
- if one player always chooses one deck, the other player will adapt by choosing the anti-deck
- therefore, the best strategy for both players, is to pick decks randomly, each with a certain probability. This type of probabilistic approach is called a mixed strategy
- if any player deviates from the equilibrium probability, then the other player can add more of the anti-deck to the deck that the other player deviated, and gain an edgeTherefore, using equilibrium probabilities is the optimal way to play
While this has some of the metrics features that Ciro Santilli wants to implement for OurBigBook.com, it limits the number of articles your readeres can read.
How the fuck can you publish on a website that limits the number of views for your articles?!?! When all it has is static pages + some metrics?!?!
Evil. Just learn to use GitHub Pages for God's sake.
A hot hot place.
Poor renaming choice.
Ciro Santilli has an undiagnozed condition where his upper legs and lower torso often start to itch when he runs, to the point of being extremely annoying and removing all pleasure form the activity.
If some doctor knows why this could be, please tell him!!!
The problem is a bit hard to reproduce however, and Ciro hasn't been able to determine which exact condition triggers it: temperature, nutrition, something else?
Ciro believes that this is not chiefly due to transpiration, but rather to the impact motion that running does on the muscles, as he has felt something similar on his arms some times while cycling in very rough terrain, which made his arms shake in a similar fashion. or for example if he has a water bottle on a tightly tied backpack that rubs his back, then the back itches at that point.
Also, running on a threadmill is not a problem at all. Ciro believes that this is because the threadmill is better amortized, and therefore does not cause the same mechanical stress required to create the itching as running on pavement.
Interestingly, Ciro didn't feel that at all when he played soccer enthusiastically as a child, and he was one of the fastest runners of the group for sure at that time. So he's not sure if it started when he got older, or if it is just because the difference in workloads between soccer and running.
Found: www.healthline.com/health/fitness/runners-itch which names "runner's itch".
youtu.be/PNgYW5N95z8?t=945 "My back itches" after riding on a bumpy makeshift motorcycle.
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