Please note that I am exceptionally talented in over-complicating even the simplest of topics, however this may be worth a read. Also, the following operations are only performed with positive integers.
The simplest operation that increases value is addition. $x+y$ can be represented as $x+(1+1+1+1...)$, "$1$" repeating $y$ times. The next operation that increases is multiplication. Similarly, $x*y$ can be represented as $x+x+x+x...$ repeating $y$ times. This pattern follows with exponentiation: $x^y=x*x*x*x...$ Using this pattern, one can find tetration. $x^{x^{x^x...}}$ $y$ times. Now let's label every item in the pattern with some degree:
{Addition:$0$, Multiplication:$1$, Exponentiation:$2$, Tetration:$3$}. Now to find some universal method to represent any degree in the continued list given two operands.
$\lambda$ seems like a good idea as it has 3 lines protruding from i. We can represent any of these operations like so:
$n$ being the degree of operation.
$x^y$ can be represented as 
because exponentiation is the second degree.
Now consider the following:
TLDR (not a sufficient one)
If the degree of iteration is infinite, and the operands are integers greater than one, will the output always be infinity?