Use the whole infinite real periodic sequence with nonempty period_values=[19, -20, 21/2], starting at index0 and repeating that full block forever. This is a declared infinite law, not an observed finite prefix. Give (period_values, absolute_bound, whole_sequence_bounded, certificate).
G001 — Use the whole infinite real periodic sequence with nonempty period_values=[19, -20, 21/2], starting at index0 and repeating that full block forever. This is a declared infinite law, not an observed finite prefix. Give (period_values, absolute_bound, whole_sequence_bounded, certificate).
Definition and scope
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ORIGINAL period index=0;value=19;absolute value=19
After
prefix absolute maximum after this original entry=19
Conditions: none
Scan absolute values over the full period rather than the maximum signed value.A negative entry may determine the bound;retain original positions and duplicates.
ORIGINAL period index=1;value=-20;absolute value=20
After
prefix absolute maximum after this original entry=20
Conditions: none
Scan absolute values over the full period rather than the maximum signed value.A negative entry may determine the bound;retain original positions and duplicates.
ORIGINAL period index=2;value=21/2;absolute value=21/2
After
prefix absolute maximum after this original entry=20
Conditions: none
Scan absolute values over the full period rather than the maximum signed value.A negative entry may determine the bound;retain original positions and duplicates.
ORIGINAL NONEMPTY full period=[19, -20, 21/2];period length=3
After
for EVERY n>=0,unique n=3q+r with0<=r<3 gives a_n=period_values[r];therefore |a_n|<=20
Conditions: none
Whole-sequence boundedness follows from the declared infinite periodic law and division with remainder,not observed future behavior.This proves the stated model,not the general Bolzano-Weierstrass theorem from finite samples.
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This question review and source binding
Review date: 2026-10-26
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