FP-Syd presentation

[thsutton]

• [ ] $1 = {}$ is the same as $0 = {}$. Missing a succ?
• [ ] The non-countability of the reals probably needs a diagram.
• [ ] I understand the non-associtivity proof is true, but I don't understand that it follows from what's been said so far; you might need to belabour some points to make this a demonstration (to me) rather than just recalling a fact I've memorised. Perhaps a sketch of the density of the floating point numbers to illustrate the whole "high precision near 0, progressively lower further away" thing around line 180? Then it's clear from the rounding behaviour.

That's pretty much it: a typo and two things that could use diagrams (which I suspect you're already planning to draw on the white board). :-)

I'm looking forward to see it!

[certifiedwaif]

Thanks Thomas, really good feedback. I'll address each of your points in turn.

1) You're right, I'll fix that. 2) Maybe you're right, graphical illustrations really help some people. I might give you a call or something and we can discuss what kind of diagram might help. The argument is essentially that the reals cannot be countable, because the unit interval isn't countable. And the reason for that is that you can construct numbers in the unit interval which don't appear on any enumerated list. 3) Indeed. There are several missing slides that I'll type up tonight or in the next day - which make up the bulk of the first chapter from a good text on numerical analysis. The argument is elementary, but does take a while to develop, so I'll write it quite carefully. It's the main result I want to present in my talk.

I was planning to do a diagram in TikZ, which my friend Charles Gray aka @tredligrrl has been teaching me.

[thsutton]

For the countability argument I think a $n \time m$ matrix of digits with $\d{1}, \d{2}, \ldots$ below it and highlighting the digits which correspond to each $d_{n}$ would do the trick. I'm pretty sure you drew a similar presentation at Anchor at least once. :-)

For the other I was thinking about something like the number line in Floating Point Demystified which lines the very low precision floating points numbers and natural numbers up, illustrating the lost of precision as the magnitude increases (it's the third image down). A proof by contradiction using that (e.g. $8 + 1.5 + 1.5$ on that number line) should make it accessible to everyone in the audience.

[certifiedwaif]

Thanks, I added the matrix. I pushed a new version which addresses some of your criticisms. Could you take a look? Thanks.

[thsutton]

Little typo: you defined succ but use s where you're encoding nats in ZFC but I think the changes are great!

[certifiedwaif]

Pushed another new version. That one's a lot better, I think.

[thsutton]

I'll try to take another look tonight but looks nice so far.

[certifiedwaif]

Thanks for spotting the typo with succ, now fixed.

[thsutton]

Looks berry nice. Looking forward to it!

[certifiedwaif]

Thanks Thomas. Just another diagram and some final editing to do, and then I can start practicing it.