
Believe It, Then Don’t: Toward a Pedagogy of Discomfort - bit-player
https://mathenchant.wordpress.com/2016/03/16/believe-it-then-dont-toward-a-pedagogy-of-discomfort/
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justin_vanw
Towards? This kind of pedagogy is nothing new. Isn't this just part (maybe the
main part, along with being able to evaluate proofs) of learning higher
mathematics? Being forced to develop an intuition like this?

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im3w1l
In an ironic twist, the pigeonhole principle itself breaks down for large
enough sets (if we phrase it as bijection between set and set with one more
element). Well the sets have to be infinitely sized for the principle to break
down, but still. So, in the vein of the article, let me ask: how do we
_really_ know the pigeonhole principle works for large but finite sets?

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justin_vanw
It certainly isn't ironic nor is it a breakdown, the pigeonhole principle is
stated on finite number of containers and a finite number of pigeons.

However, if you just arbitrarily change it around, you may well find that the
new statement you just generated is not true any more, if it even makes sense
at all.

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im3w1l
It's ironic from my point of view because the article cautions against hasty
generalizations, and that was a generalization I implicitly did upon first
hearing about Hilbert's paradox of the Grand Hotel.

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basicplus2
using cm browser cb.ksmobile.com tells me its a fraudulent phishing site

