Part of the motivation letter required by some American universities explaining how amazing of a teacher you are, e.g.: wstein.org/job/Teaching/index.html
Predicted by the Dirac equation.
We've likely known since forever that photons are created: just turn on a light and see gazillion of them come out!
Photon creation is easy because photons are massless, so there is not minimum energy to create them.
The creation of other particles is much rarer however, and took longer to be discovered, one notable milestone being the discovery of the positron.
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
- variable assignments
- addition and subtraction
- integer comparisons and if/else
- for loops
for (i = 0; i < n; i++)
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.
Luckily, early teens Ciro Santilli was partly protected from this by Ciro Santilli's cheapness.
But Ciro distinctly remembers one day in his early teens that he couldn't sleep very well, and he got up, and the was decided that he would become the greatest Magic: The Gathering player who ever lived. Can you imagine the incredible loss that this would have been to humankind? And talk about the incredible lack of development opportunity present in poor countries, related:
There are unlisted articles, also show them or only show them.