Nuprl Definition : discontinuous
discontinuous(f;x) ==
∃epsilon:{e:ℝ| r0 < e} . ∀delta:{e:ℝ| r0 < e} . ∃y:ℝ. ((|x - y| < delta) ∧ (epsilon < |(f x) - f y|))
Definitions occuring in Statement :
rless: x < y,
rabs: |x|,
rsub: x - y,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
natural_number: $n
Definitions occuring in definition :
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
int-to-real: r(n),
natural_number: $n,
exists: ∃x:A. B[x],
real: ℝ,
and: P ∧ Q,
rless: x < y,
rabs: |x|,
rsub: x - y,
apply: f a
FDL editor aliases :
discontinuous
Latex:
discontinuous(f;x) ==
\mexists{}epsilon:\{e:\mBbbR{}| r0 < e\}
\mforall{}delta:\{e:\mBbbR{}| r0 < e\} . \mexists{}y:\mBbbR{}. ((|x - y| < delta) \mwedge{} (epsilon < |(f x) - f y|))
Date html generated:
2016_05_18-AM-11_13_26
Last ObjectModification:
2015_09_23-AM-09_18_42
Theory : reals
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