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MIT PRIMES/Art of Problem Solving

CROWDMATH 2023: Arithmetic of Power Monoids

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Arithmetic of Power Monoids J
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CharmaineMa07292010
2 posts
#1
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What I've tried so far:
I've tried to consider a few cases in the set N ( positive integers) and showed that it was true. I then moved on to show that this is true for k integers in each set.

<Describe what you have tried so far here. That way, we can do a better job helping you!>

Where I'm stuck:
I don't know how I can prove that the statement is true for any set S.

<Describe what's confusing you, or what your question is here!>
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WilsonLiuwz
2 posts
#2 • 1 Y
Y by felixgotti
I guess you can apply set theory to a general proof for any set.
(pls correct me if there's any problem with my proof)
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Btw, I think this feature is a bit similar to the one of subspace in vector space.
This post has been edited 1 time. Last edited by WilsonLiuwz, Sep 13, 2023, 4:19 PM
Reason: hide my solution
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CharmaineMa07292010   1
N Sep 13, 2023 by WilsonLiuwz
What I've tried so far:
I've tried to consider a few cases in the set N ( positive integers) and showed that it was true. I then moved on to show that this is true for k integers in each set.

<Describe what you have tried so far here. That way, we can do a better job helping you!>

Where I'm stuck:
I don't know how I can prove that the statement is true for any set S.

<Describe what's confusing you, or what your question is here!>
1 reply
CharmaineMa07292010
Aug 30, 2023
WilsonLiuwz
Sep 13, 2023
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Casework
CharmaineMa07292010   1
N Sep 13, 2023 by WilsonLiuwz
What I've tried so far:
I've tried to consider a few cases in the set N ( positive integers) and showed that it was true. I then moved on to show that this is true for k integers in each set.

<Describe what you have tried so far here. That way, we can do a better job helping you!>

Where I'm stuck:
I don't know how I can prove that the statement is true for any set S.

<Describe what's confusing you, or what your question is here!>
1 reply
CharmaineMa07292010
Aug 30, 2023
WilsonLiuwz
Sep 13, 2023
J