Unfortunate Mathematical Names | The Everything Seminar

]]>i am taking the sum 1 + 1 + 1 + … as a way of “counting” the of natural numbers, such as the sum of catalan numbers was for trees.

the sum is s = -1/2, yet I would expect:

s ^ 2 = s (isomorphism between natural numbers and pairs)

s ^ 3 = s (isomorphism between natural numbers and triples)

etc

which would only hold in the case s = 1

anyone seeing something wrong in my approach?

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What I don’t get is that for each and every sequence, there exists an identical sequence with a different starting hat. So you can never know which EC you’re in, only which EC everyone in front of you is in. So you can never know what to say.

What am I missing? Please help…

(Btw Stan I love the link you posted on May 24!)

]]>For instance

101001000… may appear to be equivalent to 010010001…

for the first person but not to the second person

I am not sure if this changes anything but it is another weird aspect to this.

Also, one thing that isn’t clear is if the prisoner’s no their position in line. When guessing are they do as if they are in the first position or in the same corresponding position that they actually are in?

Lastly, isn’t each person’s guess irrelevant? Since any person who can see an infinite part of the sequence in front of them must be in the finite part? Or do these finite difference not necessarily occur at the beginning?

]]>The theorems are all of the form “a strategy exists”, as opposed to: “the prisoners can formulate some sort of strategy telling them how to behave depending on the hats that they see”. A strategy is a certain set-theoretic object. ZFC asserts ONLY that this object exists as a set (not that it can be “found” or used as an actual algorithm procedure).

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