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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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DouDragon
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Y by felixgotti
Hi, I'm just reading over the resources. I don't quite understand what a unit of $M$ is. Can someone explain?
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WilsonLiuwz
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Could you please share more information about "unit" and M you mention, maybe like the scenario?
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PiGuy3141592
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Y by DouDragon, WilsonLiuwz, Liontiger, felixgotti, Number_Basher
To say an element of a monoid is a "unit" is the same thing as saying that it is invertible. These are just two different words we use for the same concept, so the set of units of M, which is denoted $\mathcal{U}(M)$ in the preliminary resources, is the same as the set of invertible elements.
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Are all numerical monoids finitely generated?
Number_Basher   1
N Nov 22, 2023 by Number_Basher
Are all numerical monoids finitely generated? My intuition agrees with the statement, but I cannot formulate a proof.
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Number_Basher
Nov 22, 2023
Number_Basher
Nov 22, 2023
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DouDragon   2
N Oct 11, 2023 by PiGuy3141592
Hi, I'm just reading over the resources. I don't quite understand what a unit of $M$ is. Can someone explain?
2 replies
DouDragon
Sep 29, 2023
PiGuy3141592
Oct 11, 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
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