Nuprl Lemma : rnexp-converges
∀x:ℝ. ((|x| < r1) ⇒ lim n→∞.x^n = r0)
Proof
Definitions occuring in Statement :
converges-to: lim n→∞.x[n] = y,
rless: x < y,
rabs: |x|,
rnexp: x^k1,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n
Definitions unfolded in proof :
rdiv: (x/y),
true: True,
less_than': less_than'(a;b),
uiff: uiff(P;Q),
req_int_terms: t1 ≡ t2,
itermConstant: "const",
le: A ≤ B,
rnonneg: rnonneg(x),
rleq: x ≤ y,
squash: ↓T,
sq_stable: SqStable(P),
real: ℝ,
subtype_rel: A ⊆r B,
top: Top,
not: ¬A,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
guard: {T},
rneq: x ≠ y,
uimplies: b supposing a,
nat_plus: ℕ+,
sq_exists: ∃x:A [B[x]],
rless: x < y,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
or: P ∨ Q,
decidable: Dec(P),
and: P ∧ Q,
exists: ∃x:A. B[x],
prop: ℙ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
int_upper: {i...},
nat: ℕ,
converges-to: lim n→∞.x[n] = y,
ge: i ≥ j ,
so_lambda: λ2x.t[x],
so_apply: x[s],
nequal: a ≠ b ∈ T ,
rev_uimplies: rev_uimplies(P;Q),
rge: x ≥ y,
less_than: a < b
Latex:
\mforall{}x:\mBbbR{}. ((|x| < r1) {}\mRightarrow{} lim n\mrightarrow{}\minfty{}.x\^{}n = r0)
Date html generated:
2020_05_20-AM-11_09_29
Last ObjectModification:
2020_03_20-PM-01_24_22
Theory : reals
Home
Index