Teacher: See, I told you there were real world applications for limits
this post was submitted on 17 Jul 2025
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Thankfully there is a finite number of hairs, if we don't consider hair length as another variable
Zeno's Barber
The sum of all haircuts is 2.
1, surely?
If you sum the hair removed from one lil guy you'll get 1. If you sum the hair removed from all lil guys you'll get the amount of lil guys.
But yeah, you're right. I think they're looking at the problem differently. We don't care about how much hair it has at each step. It can't gain hair from a hair cut.
Maybe it would make more sense if I said "Hairdos"?
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.
No, I do mean more steps, because homeopathy dilutes a smaller volume of target material, they actually would perform fewer steps than dilution via halving.
Homeopathy often dilutes by taking far less than half of a solution and diluting it in a large amount of fresh solvent. One process repeatability empties the entire container and refills it with solvent.
If you were diluting something by replacing only half with solvent, you'd have to do many more steps to get as pure solvent as homeopathy produces.
Homeopathy is a tremendously wasteful way of washing a container. It's hugely wasteful, and being a homeopathic environmentalist is oxymoronic.
That’s exactly what I mean.
The soda dilution by halves would have far more dilution steps to reach pure water than homeopathy.
Ah. I read you backwards, by bad.
All good, language is freakin hard, man!
All that matters is we got there in the end :)
I get benefits from sugar water alcohol.
What about the shaking? If you don't aCTiVate it, it won't work.
Hmm good call, infinite soda hack!
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
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
Finite number of atoms as well, and yet scientists can split those too.
At this point you’re splitting hairs… wait…
You madlad. This is the greatest comment I’ve ever seen
I remember a comedian that had a joke similar to this. He had a volunteer come on stage, handed them a piece of paper and ask them to rip it in half. Then he told them "continue to rip it in half and eventually you'll hear a large Bang".
I mean technically there isn't a finite number of atoms because there isn't a finite number of anything because everything is part of the same energy field with varied energy states caught in self reinforcing patterns and when you "split" an atom you simply break the pattern allowing rapid entropy to a stable state.
Tldr: the solution to this paradox is that it is impossible to split anything in half, you can only rearrange it.
Zeno tried to warn us, but did we listen? Noooooo!
Well, I listened to half of his argument...
"The haircut does not exist!"
"this is going to take forever"
https://en.wikipedia.org/wiki/Zeno%27s_paradoxes?wprov=sfla1
beat me to it
Should have centered your axis around the global center instead of the local center.
Go six to eight times, then ask another barber to do the rest and a huge discount.
I volunteer to shave the guinea pigs
A supertask!
Only if each round of shaving, including the walking in and out, all take half as much time each round
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