Recent content by MeyCey

  1. M

    Ε-δ proof: lim x->a f(x) = lim h->0 f(a + h)

    Ok, so the full proof would read: By the definition of limit: \lim_{x\to a} f(x) = L_1 \iff \forall ε > 0 \ \exists δ_1 > 0 \ : \ 0 < |x - a| < δ_1 \implies |f(x) - L_1| < ε And \lim_{h\to 0} f(a + h) = L_2 \iff \forall ε > 0 \ \exists δ_2 > 0 \ : \ 0 < |h - 0| = |h| < δ_2 \implies |f(a...
  2. M

    Ε-δ proof: lim x->a f(x) = lim h->0 f(a + h)

    Oh, so the first line of a complete proof should read: \lim_{x\to a} f(x) = L_1 \iff \forall ε > 0 \ \exists δ_1 > 0 \ : \ 0 < |x - a| < δ_1 \implies |f(x) - L_1| < ε And the rest would have to be corrected analogously. Is it correct now, or am I still missing something?
  3. M

    Ε-δ proof: lim x->a f(x) = lim h->0 f(a + h)

    Yes, I understand that the proof is not complete; I omitted the quantifiers for the sake of brevity. My question was intended to be more in line of 'Is my reasoning correct?' than 'Is the proof a complete, rigorous proof?', i.e. is all I have to do from that point on is add the correct...
  4. M

    Ε-δ proof: lim x->a f(x) = lim h->0 f(a + h)

    This is a simple exercise from Spivak and I would like to make sure that my proof is sufficient as the proof given by Spivak is much longer and more elaborate. Homework Statement Prove that \lim_{x\to a} f(x) = \lim_{h\to 0} f(a + h) Homework EquationsThe Attempt at a Solution By the...
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