In the proof for the inductive step, we start by assuming $k \ge 10$. But along the way, the author mentions $k \ge 1$ and $k \ge 7$ to justify the inequality.
Why do we bother to do this instead of just sticking with $k \ge 10$?
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@G.Bach I don't think this is a duplicate as although the image is the same, the question asked is targeted at a different aspect of the solution. – mauna Jun 26 '14 at 14:50
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You should edit your other question instead of making a new one for any new aspects you'd like to ask about. – G. Bach Jun 26 '14 at 14:51
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Okay. Should I delete this question? – mauna Jun 26 '14 at 15:00
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Because in those cases all that was needed was to show that $k\geq1$ or $k\geq7$, which is obviously true if $k\geq10$. The author was simply stating the minimum required for the inequality to be true at each stage.
Silynn
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Giving exact limits is a way to evidence having thought about the other conditions, I guess – John Fernley Jun 26 '14 at 14:48