One-hot word embedding

Using a dictionary of words $V$ with $|V|$ distinct word, a one-hot word embedding will assign a one-hot vector of dimension $|V|$ to each word of dictionary $V$

$$V=\{\text{apple, durian, mango, orange, strawberry}\}$$$$f(\text{apple})=e_1=(1,0,0,0,0)$$

In this example, it is represented by a function $f:V\to O{H}_{{\mathbb{R}}^5}$, with $O{H}_{{\mathbb{R}}^5}$ being the set of all possible one-hot vectors of dimension $|V|=5$.