Things to mention while giving a talk about dedekind cuts

[samspotting]

So for an undergrad talk, I am going to present the proof of dedekind cuts. Besides proving that it makes an ordered field containing the rationals with the least upper bound property, what else could I saw to spice things up a bit?

 

[Tac-Tics]

So for an undergrad talk, I am going to present the proof of dedekind cuts. Besides proving that it makes an ordered field containing the rationals with the least upper bound property, what else could I saw to spice things up a bit?

You might want to give motivation for it.

I would start with explaining why decimals don't cut it (non-unique representation). Then, start from the rationals. Remind your audience that given ANY two rationals, they know an algorithm to add, subtract, and multiply them. But they have no such algorithm for irrational numbers. Even something simple as pi + pi... how can you show that this is equal to 2*pi? "Obviously", it's a rule from algebra. But how do you know if this "rule" holds without knowing precisely what a real number IS?

Answer: dedekind cuts let you do just this.