Eruvin, Chapter 4, Mishnah 4. This Mishnah deals with someone who established his Shabbos resting place on the road, and afterwards discovered that he was in fact standing within the boundary of a city without having realized it.
The case in the Mishnah:
A person was traveling on the road on Friday afternoon. Shabbos began while he was sitting on the road, thinking that he was outside the boundary of any city. He then stood up and saw that he was near a city, and it turned out that he was in fact within that city's boundary.
The opinion of Rabbi Meir:
The Mishnah says: "Ho'il velo haysah kavanaso lechach" - since it was not his intention to establish his resting place in the city, "lo yikanes" - he may not enter. Practically speaking, since he is within two thousand cubits of the city, he is permitted to enter it, for it lies within his two thousand cubits; but he may not walk about within the city beyond those two thousand cubits. These are the words of Rabbi Meir.
The opinion of Rabbi Yehudah:
"Yikanes" - Rabbi Yehudah permits him to enter the city.
His status is like that of the city's residents - and not only that, but his status is that of one who established his resting place in the city itself: he is like all the people of the city, and he has two thousand cubits in every direction from the city.
The reason for this is that the acquisition of his resting place where he was standing was made in error, for had he known at the time that he was within the city's boundary, his intention would have been to establish his resting place in the city.
The incident involving Rabbi Tarfon:
To strengthen his position, Rabbi Yehudah cites an actual incident: "Ma'aseh hayah venichnas Rabbi Tarfon belo miskaven" - Rabbi Tarfon entered a city and conducted himself as one of its residents, like someone who had intended from the outset to rest in the city, and he made use of the entire city, even though he had not been aware at the beginning that he was within its boundary.
In summary: In this Mishnah we learned the law of one who established his resting place on the road thinking that he was outside any city boundary, and it turned out that he was within the boundary of a city. According to Rabbi Meir, since it was not his intention to rest in the city, he may walk within it only as far as his two thousand cubits extend. According to Rabbi Yehudah, he may enter, and his status is that of one of the city's residents, with two thousand cubits in every direction from it, since his resting place where he stood was acquired in error - as he proves from the incident of Rabbi Tarfon, who entered a city unintentionally.