Ciro Santilli @cirosantilli 40

In intuitive terms it consists of all integer functions, possibly with multiple input arguments, that can be written only with a sequence of:and such that n does not change inside the loop body, i.e. no while loops with arbitrary conditions.

n does not have to be a constant, it may come from previous calculations. But it must not change inside the loop body.

Primitive recursive functions basically include every integer function that comes up in practice. Primitive recursive functions can have huge complexity, and it strictly contains EXPTIME. As such, they mostly only come up in foundation of mathematics contexts.

The cool thing about primitive recursive functions is that the number of iterations is always bound, so we are certain that they terminate and are therefore computable.

This also means that there are necessarily functions which are not primitive recursive, as we know that there must exist uncomputable functions, e.g. the busy beaver function.

Adding unbounded while loops of course enables us to simulate arbitrary Turing machines, and therefore increases the complexity class.

More finely, there are non-primitive total recursive functions, e.g. most famously the Ackermann function.

The opposite of idealism.

A way to write the wavefunction $\psi (x)$ such that the position operator is:i.e., a function that takes the wavefunction as input, and outputs another function:

If you believe that mathematicians took care of continuous spectrum for us and that everything just works, the most concrete and direct thing that this representation tells us is that:equals:

One of the main reasons why physicists are obsessed by this topic is that position and momentum are mapped to the phase space coordinates of Hamiltonian mechanics, which appear in the matrix mechanics formulation of quantum mechanics, which offers insight into the theory, particularly when generalizing to relativistic quantum mechanics.

One way to think is: what is the definition of space space? It is a way to write the wave function ${\psi }_x(x)$ such that:And then, what is the definition of momentum space? It is of course a way to write the wave function ${\psi }_p(p)$ such that:

physics.stackexchange.com/questions/39442/intuitive-explanation-of-why-momentum-is-the-fourier-transform-variable-of-posit/39508#39508 gives the best idea intuitive idea: the Fourier transform writes a function as a (continuous) sum of plane waves, and each plane wave has a fixed momentum.

Bibliography:

This is a porn style defined by Ciro Santilli as:Ciro believes that this is an interesting type of pornography, as it feels more natural and humane than all the horrible trash that comes out of horrendous professional mainstream porn industry.

Yes, it could go down the YouTube/Instagram alley, and lead the vloggers to do things they wouldn't normally do because of the audience. But who is to say that Ciro Santilli doesn't do the same on Stack Overflow to some extent?

That type of porn requires some big courage to make. Or balls if you will. Kudos to those creators, as it is so taboo it could greatly impact their future job prospects.

The travel sex vlog appears to be the most popular way to do it. Presumably the reason being that you would not be able to interact with people in a normal job, so to keep things interesting you need to go to some random places.

Examples:

Bibliography:

Basically mean that parallel evolution happened. Some cool ones:

By default, we think of polynomials over the real numbers or complex numbers.

However, a polynomial can be defined over any other field just as well, the most notable example being that of a polynomial over a finite field.

For example, given the finite field of order 9, $GP(3)$ and with elements $\{0,1,2\}$, we can denote polynomials over that ring aswhere $x$ is the variable name.

For example, one such polynomial could be:and another one:Note how all the coefficients are members of the finite field we chose.

Given this, we could evaluate the polynomial for any element of the field, e.g.:and so on.

We can also add polynomials as usual over the field:and multiplication works analogously.

Positive center is way more popular: gearspace.com/board/electronic-music-instruments-and-electronic-music-production/1222518-center-negative-vs-center-positive-power-supply.html

One of the main children cartoons Ciro Santilli liked to watch. Part of the Pokemon Mania of the 90s of course.

Ciro could not understand why Nintendo won't make a proper 3D MMORPG Pokemon with actually 3D Pokemon roaming the land, which is obviously what everyone wants. There are even fan games getting there!until this explaiend it beautifully Video 1. "The Downfall Of Mainline Pokemon Games by GONZ media (2020)":

Generalization of Laplace's equation where the value is not necessarily 0.

The first working one in 1947 by John Bardeen and walter Brattain in Bell Labs Murray Hill.

People had already patented a lot of stuff before without being able to make them work. Nonsense.

As the name suggests, this is not very sturdy, and was quickly replaced by bipolar junction transistor.