# Why does frequency equal k/K where k=0,…, K-1 in Discrete Fourier Transform?

I totally can't understand why f = k/K. What does k, K means, respectively?. I really want to know what they actually indicate in real world. Or, please give me an example. I spent 2 days night but could't catch the DFT.

The DFT is, essentially, a sampled DTFT where the number of samples is $K$ and, thus, the spectrum is sampled at frequencies with spacing proportional to $\frac{1}{K}$ or, as in the image below, $\frac{1}{N}$
Note the $k$ indexes the samples in frequency just as $n$ indexes the samples in time.