- #1

picketpocket826

- 2

- 0

The above two video from numberphile are trying to motivate real analysis (I think?). The latter continues on from the former.

Presenter's argument goes kind of like this:

He first considers the real number line and talks about measuring distance between numbers

4-3=1

Then he talks about measuring the length of points and takes 3.5 as an example.

3.5-3.5=0

Then supposes that if you removed the point 3.5, the length of 4-3 stays the same and the number line remains unchanged.

(He doesn't actually say this next part but it's implied)

However, if you remove the length between 4 and 3, then there is indeed a change to the number line.The he states this inconsistency almost broke maths.

The major problem here being that there is no "next point" after 3.5

**So my question:**

1. Is this a valid argument (that motivates real analysis) ? I can't help but not be convinced but it is interesting. Brady (guy interviewing) argues if he removes someone's feelings their size wouldn't change and likewise if he removes points from the number line it shouldn't change in size either since points are abstractions. Although there is a kind of counter to this argument - feelings do have a physical substrate so removing them would at least change a person's weight if not their size.

Edit: I realised he kind of explains at the end.

Last edited by a moderator: