this post was submitted on 07 Sep 2024
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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.
There's notation for that - (x0 - δ, x0 + δ), so you could say
f(x0 - δ, x0 + δ) ⊂ (L - ε, L + ε)
that would be a lot clearer. i’ve just been burned in the past by notation in analysis.
my two most painful memories are:
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.
Egregious. I feel your pain.