My friend answer the following:

The relevant sense of traversing an infinity means to have completed an infinite number of tasks (or steps) or to have experienced an infinite number of events. If you mean anything else by the term, then you need to show why traversing an infinity is required in order for time to be past-infinite. So, is it true that in order to have completed an infinite number of tasks "there would always be one more" task needed for the completion? If so, it's not clear why. You claim that otherwise there would only be finitely many tasks. But---again---what makes you think that?

In fact, it's fairly easy to show that these claims are false. All we need to do is show a counter-example. So here's one: Let t(0) denote the present moment, and let t(-1), t(-2), t(-3), ..., denote successive past moments, on ad infinitum. Suppose Xenophon has been alive all this time, experiencing these successive moments passing. Then for any n, at t(-n) Xenophon has already experienced an infinite number of temporal successions, i.e. he has already traversed an infinity. At no point does he need to complete another task in order to complete the traversal. since the traversal has always been completed.

Perhaps I am misunderstanding his point, but I don´t think this example is correct. But i can not pinpoint exactly what is wrong in his example if there is anything wrong with it.

So for the time example, would that be a set of events or, would it be an x going to infinity.

by w+1 I meant (omega+1). for me w+1 sorry I don´t know how to print that symbol omega+1 = {x| x finite or x=omega}

My friends says that not all infinite numbers are limits and offers omega+1 as an example.

Thanks a lot ,for your answers and help.