Is it possible to use the numbers 2, 0, 1 and 3 only once and use any arithmetic functions (+, -, *, /, indices, decimals, factorials, trig etc.) to make integers from 1 to 100?
For example:
and so on...
Note: You can put the numbers together in the beginning (like 20+13=33), but you can't do it afterwards (like 2+0+1=3, and then you put a 3 at the end to make 33).
The solution probably depends on what exactly is in the "etc". If we have functions $\exp$ and $\ln$, then we can obtain any natural number this way: $$ n = - \frac{\ln\left(\ln\left(\sqrt{\sqrt{\ldots\sqrt{\exp(1)}}}\right)\right)}{\ln 2} $$ if $n$ is the total number of radical signs ($\sqrt{}$).
I didn't use $3$ and $0$ though. If it is obligatory, then you can just add $3-0$ in the end and still get all the natural numbers starting from $3$. Or even better, you can add $0-3$ in the end and throw in three more radical signs to compensate.
