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Elementary inequality

  1. Nov 5, 2008 #1
    I'm looking over a proof and I'm wondering from which principles does it follow that
    [tex] \mid a - b \mid < 1 \to \mid a \mid < \mid b \mid + 1 [/tex]

    I can see that [tex] |a - b | \le |a| + |-b| = |a| + |b| [/tex] and that [tex] |a| - |b| < |a| + |b| [/tex] but I just can't connect the dots.
  2. jcsd
  3. Nov 5, 2008 #2

    Ahh, got it [tex] |a| = |(a+b)-b| \le |a-b| + |b|[/tex] which means [tex] |a| - |b| \le |a-b| [/tex] the result immediately follows
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