1/2 off haircuts

Teacher: See, I told you there were real world applications for limits

The real question is, to how many iterations does the hamster say "Eh, good enough"
- It's a guinea pig!
- Well, "hairs" are quantized phenomenon...
  So at some finite time, it will be all gone. At least if the thing is happening fast enough for it not to grow back at a similar time-frame.

When I was a kid I encountered this problem when I wondered what would happen if I half-empty a bottle of soda, re-fill it with water, and repeat. Will it eventually become just water or will there always be some soda left? It boggled my mind for a while, then I forgot about it until I reached university calculus haha

You invented homeopathy! Just with more steps (literally).
- You mean less steps. True homeopathy dilutes until there's no measurable amount of the substance left; it's just pure sugar/water/alcohol. You're supposedly getting benefits from "the vibrations."
  Of all the pseudo-science quackery, homeopathy is one of the most idiot-prone.
- What about the shaking? If you don't aCTiVate it, it won't work.
- A little too accurate?
  https://www.youtube.com/watch?v=HMGIbOGu8q0
The answer is that eventually all trace of the soda would be gone because there are only a finite number of atoms of "soda-stuff" and eventually you'll end up with a situation where there's only one molecule left, which - assuming that wasn't the water part of soda in the first place - will have a 50% chance of being in the half that's removed before the next dilution step. Theoretically it could survive infinitely many rounds of this, but the chance of that is basically zero.
How many times is that though? For a litre of soda, the lower bound is about 85. A hundred ought to be more than enough. (And 300 times would be enough to dilute the entire observable universe assuming it was soluble in water, so that's a reasonable upper bound.)
You'd almost certainly stop tasting the soda quite a while before that though. After 20 dilutions you're into parts per million soda to water.
Things become more complicated if you replace the soda in this experiment with holy water. It seems to be agreed that 50/50 holy to regular water remains holy, but after that, some believe that dilution can be repeated forever (presumably being left to sit for a while after that step) while others claim the holiness disappears once the dilution goes beyond 51%, regardless.
- It's easy to test for water holiness. If you drop the bottle and it bursts into flame molotov-cocktail style, it is still holy water.
  Source : Belmont et al., Wallachia, 1986
- "If something can happen, it will happen."

Zeno tried to warn us, but did we listen? Noooooo!

Well, I listened to half of his argument...

Zeno's Barber

Well there's a discrete number of hairs on that rodent thing, depending how the barber rounds they'll have to cut the last hair eventually. Unless they only cut half of the last hair?

... then they cut one half of the remaining half.
- Finite number of hair cells

it took me a while to understand that the guinea pig(?) in the window is meant to be the reflection of the one outside. Because the surface is roughly parallel with the viewer, the one outside is pointing to the left, so the flipped pig should also be pointing left.

Yes the artist doesnt seem to understand reflections.

"The haircut does not exist!"

A supertask!

Only if each round of shaving, including the walking in and out, all take half as much time each round

https://youtu.be/72jzfN_kMnw

This is one of those times you are hoping someone put Nair in the conditioner. It's rare to yearn for, but that little guy needs the help