Does the real line mean that the start and end points of any line must exist?

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line

https://en.wikipedia.org/wiki/Real_number

We consider the set of real numbers, denoted by R, as the points on an infinite straight line – called the real line– on which we have fixed two different points, say “0” and “1”. We consider the distance between 0 and 1 as one unit, and therefore, the points 0 and 1 define a measure on the real line. This measure has also a direction,namely from 0 to 1, denoted~01, thus, the distance between two points can also be negative. Further, we identify a point on the real line with its distance to 0 (with respect to the measure~01) and this distance is called a real number.

http://user.math.uzh.ch/halbeisen/4students/pdf/1-4.pdf

This basic maths suggests that we can't have real numbers without a real line.

But also there are no gaps in a real line. Does that mean that any point along any line must exist, including its start and end points?

I'm asking because I don't understand how the point instant of my death (at the end of life) can be said to exist. But I don't explain that, in order to stay on topic.

• This isn’t a philosophical question on the philosophy of mathematics. You might want to ask this very basic question on Math.SE. Jul 17, 2019 at 4:42
• there's no need to downvote for that reason @MoziburUllah ! feel free to migrate it tho!
– user38026
Jul 17, 2019 at 4:44
• do you know the answer @MoziburUllah ? it's clearly a question about existence anyway so i don't think it's suitable for the math SE
– user38026
Jul 17, 2019 at 4:45
• I did down-vote and why not if I disapprove of it? That’s the whole point of down-voting. If you do migrate to Math.SE you might want to clean it of it’s conceptual salad-dressing otherwise they may throw it out there too. Jul 17, 2019 at 4:56
• you're picking and choosing! does philosophy SE not ask about "existence"? @MoziburUllah and do you know the answer?
– user38026
Jul 17, 2019 at 4:58

There are really two questions here. One is a pure math question "do real numbers exist without the real number line?" The answer is most certainly yes. The properties of real numbers can be defined in a way completely independent of geometry. The number line is merely a simple geometric construct which can be used to explain some of those properties.

As for "do the start and end points exist," the study of real numbers includes the concept of an open or closed end-point. You are permitted to use open sets of points to capture the idea of a set of points that does not include its end point.

So when it comes to the instant of your death, it is not unreasonable to say that your subjective concept of time is open at the instant of your death -- you can describe what happens up to that point, but not at that point. However, if there exists an objective observer (or a subjective observe who outlives you), they may be able to talk about the instant of your death.

• that's great, thanks for the answer!
– user38026
Jul 17, 2019 at 5:25
• There is no "philosophy" here... If we model the "time line" with the continuum of the "geometric line" a human life is simply a segment with start- and end-point. No "philosophy of mathematics" involved, neither "deep meaning" about existence. Jul 17, 2019 at 7:08
• yeah it's mostly maths, but you can see why i thought it might not be @MauroALLEGRANZA ?
– user38026
Jul 17, 2019 at 9:27
• @another_name - Your attempt to link the nature of time, the real numbers and the instant of death seems a little off-beam to me, but it also seems like a valuable way to think about these things and usefully philosophical. It all comes down to the nature of the Continuum, on which topic you might like to read Hermann Weyl.
– user20253
Jul 17, 2019 at 12:23