Please help me to prove that the limit of the following function does not exist:

I've read the documentation on events, and as far as I can tell after an hour or two, I am doing exactly what is in the documentation but not getting the expected result.

Here is a worksheet illustrating the issue: dsolve_events.mw

Basically there is a very simply system of two differential equations and I would simply like to see an event triggered when the dependent variable is above 2.

This event has no useful interpretation, it was just my attempt at trying to get something to trigger (I have tried multiple things). As far as I can tell from the docs I am using an event specification of form

[0, c(t,y(x)) < 0]: discrete event with a conditional trigger

ie, [0,2-x<0]

and when that is triggered I set i(x) to something like i(x)+1 (but even something as simple as assigning it to some constant like 7, given that the initial value i(0)=0, would allow me to check when the event is being triggered), where i(x) is defined as a discrete variable (my ultimate goal is to trigger the event on every iteration and have i be the iteration counter. I want to use this iteration counter in the equations)

I run the dsolve command, assign the result to a variable *p *and then call, for example *p(3). *I would expect to see the event triggered and i(3) not equal to the initial value i(0). But the value of i(x) doesn't change.