Nuprl Definition : real-cont
real-cont(f;a;b) == ∀k:ℕ+. ∃d:{d:ℝ| r0 < d} . ∀x,y:{x:ℝ| x ∈ [a, b]} . ((|x - y| ≤ d) ⇒ (|(f x) - f y| ≤ (r1/r(k))))
Definitions occuring in Statement :
rccint: [l, u],
i-member: r ∈ I,
rdiv: (x/y),
rleq: x ≤ y,
rless: x < y,
rabs: |x|,
rsub: x - y,
int-to-real: r(n),
real: ℝ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
apply: f a,
natural_number: $n
Definitions occuring in definition :
int-to-real: r(n),
natural_number: $n,
rdiv: (x/y),
apply: f a,
rsub: x - y,
rabs: |x|,
rleq: x ≤ y,
implies: P ⇒ Q,
rccint: [l, u],
i-member: r ∈ I,
real: ℝ,
set: {x:A| B[x]} ,
all: ∀x:A. B[x],
rless: x < y,
exists: ∃x:A. B[x],
nat_plus: ℕ+
FDL editor aliases :
real-cont
Latex:
real-cont(f;a;b) ==
\mforall{}k:\mBbbN{}\msupplus{}. \mexists{}d:\{d:\mBbbR{}| r0 < d\} . \mforall{}x,y:\{x:\mBbbR{}| x \mmember{} [a, b]\} . ((|x - y| \mleq{} d) {}\mRightarrow{} (|(f x) - f y| \mleq{} (r1/r(k))))
Date html generated:
2016_07_08-PM-06_03_13
Last ObjectModification:
2016_07_05-PM-02_45_16
Theory : reals
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