Ciro Santilli @cirosantilli 37

The easy and less generic integral. The harder one is the Lebesgue integral.

As mentioned at Section "Plancherel theorem", some people call this part of Plancherel theorem, while others say it is just a corollary.

This is an important fact in quantum mechanics, since it is because of this that it makes sense to talk about position and momentum space as two dual representations of the wave function that contain the exact same amount of information.

Set of ordered pairs. That's it! This is illustrated at: math.stackexchange.com/questions/1480651/is-fx-x-1-x-2-a-function/1481099#1481099

Much of this section will be dumped at Section "Website front-end for a mathematical formal proof system" instead.

Sets are unordered, but we can use them to create ordered objects, which are of fundamental importance. Notably, they are used in the definition of functions.