What Is the Fourier Transform?

Can somebody eli5, im an amateur. How does the transform know the frequencies of the output. Do you have to specify a number n, and then it decomposes it into n frequencies. Or do you give it a list of frequencies, and then it decomposes the coefficient or amplitude or something for each?

I guess what i want to know, in the examples it always shows like 3 or 4 constituents frequencies as output, but why not hundreds or a million? Is that decided upfront /paramtetizable?

The article isn't helpful, it just says something like "all possible frequencies".

I'll try.

Suppose you blinde, and are on one side of a black picket fence. Let's say the fence uprights are 1" wide, and 1" apart.

If you aim a light meter at the fence, it will sum up all the light of the visible slices of the background. (This meter reads its values out loud!)

Suppose the background is all white - the meter sees white slices, and get a 50% reading (because the fence stripes are black). It's as high as you can get.

Now move the picket fence half an inch to the left - still all white, still a 50% reading. Now you know the background is 100% white, no other colors.

But if when you move it, black stripes are exposed, then the meter reads 0%, and you know that the background is 50/50 white and black, in stripes.

Congratulations! You've just done a Fourier transform that can detect the difference between 0-frequency and a 1"-striped frequency pattern. In reality, you're going to continuously move that fence to the left, watching all the time, but this is simple.

But instead, imagine you got readings of 40% and 10%. What kind of pattern is that? Gray stripes? White stripes that aren't as wide as the fence posts? You'll have to build another fence, with another spacing - say 1/2" fence posts 1/2" apart. Repeat.