which number corresponds to the right endpoint of line segment [0,1)?

Question

I hold two basic opinion that

(1) Every line segment has two endpoints.

(2) The endpoint of a line segment is part of it.

So as for the line segment corresponding to [0,1], if we remove its right endpoint, which number corresponds to the right endpoint of the new line segment? I don't think the number is still 1, because we have already removed the point corresponding to 1, thus created this new line segment, the point 1 is not part of the new line segment, so according to my opinion (2), I don't think the number is 1.

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Update: A bounded continuous segment in a line is my definition of "line segment"

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Update: I think I solved my question , see answer below

Answer 1

Your second "basic opinion" is simply untrue. The number is $1$.

Answer 2

Your opinions (1) and (2) are inconsistent with your (implied) opinion (3), that $[0,1)$ is a line segment. If you truly believe all three of these statements, then it follows, as night follows day, that you believe that $2+2=7$, that the Moon is made of green cheese, and that you are the Pope. I would recommend that you carefully consider your three beliefs, and see which one(s) you are really committed to, and which one(s) you are willing to abandon, in the interests of not being in a state of self-contradiction.

Answer 3

First , it is helpful to inform me to check whether [0,1) has a right endpoint after removing .

Second , just as @ShubhamJohri informed that

A line segment may not contain its end points -- it only needs to contain all points between them. Read here

so I misunderstood the definition of a line segment.

Answer 4

There strictly speaking is no endpoint of a line_segment or ray at an open boundary. That said, the real number corresponding to an end of a line_segment defined by and terminating at a finite value {be it [included or excluded)} is simply that number, i.e. 1.