Nuprl Lemma : harmonic-series-diverges
Σn.(r1/r(n + 1))↑
Proof
Definitions occuring in Statement :
series-diverges: Σn.x[n]↑,
rdiv: (x/y),
int-to-real: r(n),
add: n + m,
natural_number: $n
Definitions unfolded in proof :
so_apply: x[s],
ge: i ≥ j ,
sq_exists: ∃x:A [B[x]],
rless: x < y,
le: A ≤ B,
lelt: i ≤ j < k,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
nat: ℕ,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
decidable: Dec(P),
nat_plus: ℕ+,
cand: A c∧ B,
prop: ℙ,
true: True,
less_than': less_than'(a;b),
squash: ↓T,
less_than: a < b,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
or: P ∨ Q,
guard: {T},
rneq: x ≠ y,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
diverges: n.x[n]↑,
series-diverges: Σn.x[n]↑,
uiff: uiff(P;Q),
sq_stable: SqStable(P),
subtype_rel: A ⊆r B,
primtailrec: primtailrec(n;i;b;f),
primrec: primrec(n;b;c),
exp: i^n,
subtract: n - m,
int_upper: {i...},
top: Top,
real: ℝ,
rev_uimplies: rev_uimplies(P;Q),
rdiv: (x/y),
req_int_terms: t1 ≡ t2,
rge: x ≥ y,
assert: ↑b,
bnot: ¬bb,
sq_type: SQType(T),
bfalse: ff,
ifthenelse: if b then t else f fi ,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
nequal: a ≠ b ∈ T
Latex:
\mSigma{}n.(r1/r(n + 1))\muparrow{}
Date html generated:
2020_05_20-AM-11_21_18
Last ObjectModification:
2019_12_28-AM-11_02_27
Theory : reals
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