Same as if you are scrolling and have reached result 20 And want to load more.
There's potentially a difference if the server's sending repeat posts and you're doing client-side filtering of what to show next. But do any sites work that way?
(And of course these issues only exist when your list of results changes order. It the list merely grows then you can paginate with start=xxx)
We want visitors to imagine that we just plopped a binder of sorted results down in front of them for their page-by-page perusal, but the suggests permanence and invariants we don't want to provide (because it's harder.) For example, the assurance that page 2 will always have the same items on it unless they "search again", and the last item on page 2 will not not duplicate itself on the top of page 3 as they page forward.
By way of contrast, imagine a system where a result-set was not just a UI metaphor, but real domain concept. Do a search, and you get a Result which is a limited-size listing generated at time X for user Y and will be cached for Z.
The typical infinite scroll that I've seen implemented does not work the way you describe though, it's just pagination without controls. The reason it works is because it's pushing content you never asked for anyway and it just keeps pushing. Without any sense of pages you'll never know the difference.
Users know that they are scrolling endlessly, they just don’t care. Adding a “more” button every now and then isn’t going to change that.
[A B C] D E F G H …
where the brackets represent the first page. If the user clicks the next page button (asking for the next page after C), but meanwhile the order changed, they get this: A D C [B F E] G H …
Notice how they now see B twice and completely miss out on D. In constrast, infinite scroll will take the new infinite list and remove A B C, leaving D F E …