No you can't, not in reality. Those kind of absurdies cannot actually "happen".
I am not gonna pretend like I understand what you are saying...so instead of trying to figure it out...I will just stand by my own absurd example...and if we can imagine going in time in a time machine, and we wanted to travel EQUAL distance going backwards that would EQUAL the distance that we've traversed at lets say, 8:00 today, and we were to STOP at that exact time in the past when we've reached the distance.....at what point would we stop?
The answer is incoherent, because whatever point we stop, there was still time before it...so the distance would never be traversed!!! So we would never reach an equal point, because there were points before it that would have to be included in the total equal distance..see how that works?
So if we would never reach an equal distance moving backwards, then we can't reach any equal distance moving forward. See how that works?
Before you give me ANYTHING...i would like my examples to be addressed. If you can give an adequate response to what I said, I will be more than happy to address what you said. If you can't adequately answer my analogy, then there is no reason for me to address yours because if what you say is correct, you SHOULD be able to answer my analogy.
You absolutely can subtract infinities *which are identical* and have them cancel out. Yes, this is done often. Think of some expression which when evaluated gives you an infinite result, some specific integral. Now, simply subtract one from the other, of the exact same thing. Something really easy, say x^2 evaluated from 0 to infinity. That's clearly infinity. But, what is x^2-x^2 each term individually evaluated from 0 to infinity? 0 of course. That is what I am proposing here. We can take some reference time and say the number of events before that is infinite. we've agreed on how to divvy up time and so on, and use the same standard. Now we define all events with reference to this time, call it r.
I'm not attempting to make this purposefully difficult. My issue is, if we don't formalize them even a little, attempt to make it careful and systematic, we aren't ever going to see if this is really a problem or not. Relying on vague terms, analogies and metaphors won't cut it here. You are claiming we can't subtract 'infinities' meaningfully. Sure, if you subtract the set of odd numbers from the set of all integers, you are left with an infinite set. But, let me ask you this, what if we subtract the set of all odd numbers from the set of all odd numbers? That is, if we subtract identical sets from each other? where there is 1 in the first there is 1 in the second, subtract those, we get 0. For 3, it appears in both, we get 0, and so on. Every single one is paired. THIS is analogous to what I am saying about subtracting infinities in this case. We've agreed there are time ordered events, 1, 2, 3 and so on. I say, great, let that be infinite, now set r somewhere, and subtract off every event, one by one, each and every time we need to calculate an interval of time.
You seem to think that we can never reasonably think that we are 'at this time' if there are an infinite number of past events. But let's look at my scheme above. Give me any past event that you think that we can't get from there to here from, any one. Give me the farthest one in the past you can conceive of. I can define a finite interval of time each and every time. So really, what is the problem?