d. Choose one amo the wel- Ordering Principle, Zorn's Lemma and Axiom of Choice. Then either desonike Idireuss the chosen statement using your oun words or illustrote it using oun original example . f. Consider the set B- (N,E,P,Z, Q, Qʻ, R,R, € f, where E is the set of all even numbers, IP s the set of all prime numbers, Q s the set of all irahoral numbers , R" s the sel of all pasitire real numbers, and Cs the fet of all compex numbers. Define the partial order e B the rule : by "X
d. Choose one amo the wel- Ordering Principle, Zorn's Lemma and Axiom of Choice. Then either desonike Idireuss the chosen statement using your oun words or illustrote it using oun original example . f. Consider the set B- (N,E,P,Z, Q, Qʻ, R,R, € f, where E is the set of all even numbers, IP s the set of all prime numbers, Q s the set of all irahoral numbers , R" s the sel of all pasitire real numbers, and Cs the fet of all compex numbers. Define the partial order e B the rule : by "X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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Please answer d, f, and g.
Transcribed Image Text:d. Choose one
amo ng
the well- Ordering Principle, Zorns Lemma and Axiom of Choie. Then
Own words or illustrote it vsing
either desonike I disauss the chosen statement using your
your oun
original example .
f. Consider the set
B- (N,E,P,Z,Q, Q', R', R,C f, where E 8 the set of all even numbers,
P s the set of all prime numbers, Q° is the set of all irahional numbers,
is the sed of all
pasitire real numbers, and Cs the Fet of all complex numbers. Define the partial order E
on B by the rule :
"X4Y if and only if xl lyl or
Draw the lattice/poset drogram for (B, 5)
Bricfly describe the Continuoum Hypothens. Also, tackle how it relates to the axioms of
ZF set theory.
Transcribed Image Text:Consider the partial order "" on the set
A. { Luffy, Zoro, Sanji , Chopper, Robin, Brook, Nami', Usopp. Franky, Jinbe }
where lattice
Luffy
diagram is on
the right
Zoro
Sanji
Brook
fronky
Jinbe
Robin
Nami
Usopp
Chepper
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