Representing any number using only 0 I am afraid to even ask this question, but this is something that was asked over a breakfast table by a friend of mine.


  How do I represent a number, say 4, by using just zeros as a numeral in tandem with any function or mathematical operator(s)?


Now one way to do this is by using a factorial, since $0!=1$:
$$0! + 0! + 0! + 0!$$
Another way uses $\cos 0=1$:
$$\cos 0+\cos 0+\cos 0+\cos 0$$
Also, the topmost  $1$ on Pascal’s Triangle is the zero$^{th}$ row, zero$^{th}$ entry, i.e.,  $0C$$_0$ = $1$.

The Partition function , P(n) is , by convention , defined as $1$ for $n=0$, i.e. , $P(0) = 1$.

Is there any other way I could possibly achieve this?I would be more interested to know the functions which when applied on zero produce non-zero results , like the ones mentioned earlier in the question, rather than semantic manipulations or visual representations.
Peano says: with the successor function.

$$4=S(S(S(S(0))))$$
Changing my answer...
Per the question, use only zeroes $$\frac{\color{blue}{zero} + \color{blue}{zero} + \color{blue}{zero} + \color{blue}{zero}}{\color{blue}{zero}}$$
Note: $zero\ne0$ $\color{lightgray}{:-)}$