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  title: '"I really like this domino analogy.\n\nAlso, I'd e..."',
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  anchorContext: 'The principle of mathematical induction is a proof technique in which a statement, $P(n)$, is proven about a set of natural numbers $n$\\. It may be best understood as treating the statements like dominoes: a statement $P(n)$ is true if the $n$\\-th domino is knocked down\\. We must knock down a first domino, or prove that a base case $P(m)$ is true\\. Next we must make sure the dominoes are close enough together to fall, or that the inductive step holds; in other words, we prove that if $k \\geq m$ and $P(k)$ is true, $P(k+1)$ is true\\. Then since $P(m)$ is true, $P(m+1)$ is true; and since $P(m+1)$ is true, $P(m+2)$ is true, and so on\\.',
  anchorText: 'It may be best understood as treating the statements like dominoes',
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  text: 'I really like this domino analogy.\n\nAlso, I'd expect to see the word "all" somewhere in this first paragraph -- I think it's worth emphasizing the point that if we have the base case and the inductive step then the statement will be true for *all* of the numbers after the base case, just like all of the dominoes after the first one would fall down. I think the current final sentence of the intro paragraph doesn't make this clear enough.',
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