$2\wedge 3\wedge 4$ could be $(2^3)^4$ or $2^{(3^4)}$. Does it make any difference? For both definitions, which is bigger: $r\wedge r\wedge r\wedge r\dots$ where the powers of $r$ go on for ever, or $(r^r)^r$, where $r$ is $\sqrt{2}$?

Staircase

Stage: 5 Challenge Level:

Consider this as a sequence given by:

$$x_{n+1}=x^{x_n}$$

where $x_1=x^3$.

Now consider the sequence of equations given by $x_n=3$.