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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\\.',
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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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