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unless f(x~0~ ± δ) is some kind of funky shorthand for the set { f(x) : x ∈ ℝ, | x - x~0~ | < δ }. in that case, the definition would be “correct”.

it’s much more likely that it’s a typo, but analysts have been known to cook up some pretty bizarre notation from time to time, so it’s not totally out of the question.

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davidagain@lemmy.world ⁨3⁩ ⁨months⁩ ago
There’s notation for that - (x0 - δ, x0 + δ), so you could say
f(x0 - δ, x0 + δ) ⊂ (L - ε, L + ε)

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- affiliate@lemmy.world ⁨3⁩ ⁨months⁩ ago
  that would be a lot clearer. i’ve just been burned in the past by notation in analysis.
  
  my two most painful memories are:
  
  in the (baby) rudin textbook, he uses f(x+) to denote the limit of _f _from the right, and f(x-) to denote the limit of f from the left.
  
  in friedman analysis textbook, he writes the direct sum of vector spaces as M + N instead of using the standard notation M ⊕ N. to make matters worse, he uses M ⊕ N to mean M is orthogonal to N.
  
  there’s the usual “null spaces” instead of “kernel” nonsense. ive also seen lots of analysis books use the → symbol to define functions when they really should have been using the ↦ symbol.
  
  at this point, i wouldn’t put anything past them.
  
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  - davidagain@lemmy.world ⁨3⁩ ⁨months⁩ ago
    Egregious. I feel your pain.
    
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