How do you prove that a suitcase can hold an infinite number of hankies?
- Base case: Obviously, a single hankie will fit in a suitcase.
- Induction step: Ah well, just one more sure will fit!
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I like how a serious paradox for ancient philosophers becomes just a joke for students today. 
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“With the assumption that removing a single grain does not cause a heap to not be considered a heap anymore, the paradox is to consider what happens when the process is repeated enough times that only one grain remains and if it is still a heap. If not, then the question asks when it changed from a heap to a non-heap.”
I think the definition of “heapness” should be left up to our Australian brothers and sisters
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Ohhh… as a statistician being mildly obsessed about how pie charts often are not such a good idea to visualise your data, this is a very good one!
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This reminds me of the (not really a joke) math puzzler. Find the logical misstep in the following induction proof.
To prove:
All horses are the same color.
Base case: Consider a set of one horse. Clearly, one horse is the same color as itself, therefore a set of one horse is all the same color.
Induction step:
- Consider a set of N horses. Partition the set into a subset of 1 horse, call this horse i, and a subset of N-1 horses. By the inductive hypothesis, the N-1 horses are all the same color.
- Now re-partition the original set into a subset of 1 horse j ≠ i and a subset of the other N-1 horses. By the inductive hypothesis, the set of N-1 horses is all the same color, including, in particular, horse i.
- But we’ve previously established that j is the same color as all other horses in the set other than i. By the transitive property, horse i and horse j are thus the same color.
- Therefore, by the principle of mathematical induction, all N horses are the same color.
Now, where is the poison? The battle of wits has begun.
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Nothing rhymes with orange.
Nothing rhymes with purple.
Therefore, by induction, orange rhymes with purple.
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I was honestly confused by this. I think you must mean by the transitive property, not induction.
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