How many grains of sand do you need...
...until you have a heap of sand?
workings hint hide answer print
Is a million grains of sand a heap?
We can probably agree on two things:
1. A million grains of sand is a heap.
2. If we remove one grain of sand from a heap, we still have a heap.
We can now keep repeating #2 until we only have a single grain of sand remaining. Is this a heap? Clearly not. But what went wrong with our thinking?
This is called the Sorites paradox (soros being Greek for "heap") and is a classic paradox that has no real answer. Both #1 and #2 are true, and we can indeed keep removing one grain of sand until we have a single grain remaining. When does the heap become a non-heap? If we remove one more grain we're left with nothing, is this still a heap?
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