All mathematical theorems should be intuitively explained with animal cruelty.
this post was submitted on 30 May 2025
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That's now how this works. That's really not how this works...
I see no flaws in that logic: at least one pigeon should have more than one hole in it.
is there an upper limit for the "hole area" a pigeon can have before it can't be considered a pigeon anylonger?
I think no, as we don't have any statements about size of holes, so they might be infinitely small, making it trivial to fill a single pigeon with an infinite amount of holes.
seems like the problem is not well defined, because it might also be possible to drill a whole pigeon away, given a sufficient number of large enough holes.
I disagree. A hole is only a hole when it has an uninterrupted "edge".
Drilling "two" holes that touch makes them just one (larger) hole.
As such, if you were to drill the entire pigeon away you haven't actually created a single hole. There is no pigeon anymore so there is no hole.
If we were to only allow drilling valid holes (holes that have an uninterrupted edge) then you cannot ever drill a whole pigeon away.
Nah, all is good. You're talking about irrelevant characteristics. If you really need to link the problem to the real world, then just imagine infinitely big pigeons and infinitely small holes. See how everything became obvious and trivial?
I think you'll find that that's exactly how this works.
What are you, some kind of pigeon?
I mean, pigeons have more than one hole even before the theorem gets applied