Mathematics Asked by HEKTO on October 3, 2020

Let’s consider the set $S subset Bbb N$, consisting of all prime numbers. We can introduce a binary "addition" ($+$) operation on the power set $Bbb P(S)$, which is defined as the regular set union – so the set $Bbb P(S)$ becomes a monoid. It’s easy to see that all the elements of the set $Bbb P(S)$ can be thought as natural numbers, for which all the primes in their factorization *aren’t repeated*. So, adding $2$ and $2$ *in this monoid* gives us $2$:

$$2+2 = 2$$

Also, the number $4$ doesn’t belong to the $Bbb P(S)$, because its factorization contains $2$ to the second power.

Does this monoid have a name?

1 Asked on January 29, 2021 by mk7

curves differential geometry riemannian geometry submanifold surfaces

3 Asked on January 29, 2021 by ramez-hindi

discrete mathematics elementary number theory factorial inequality

1 Asked on January 29, 2021 by siddharth-bhat

2 Asked on January 29, 2021

1 Asked on January 28, 2021

1 Asked on January 28, 2021 by inoc

integration lebesgue integral real analysis trigonometric integrals

1 Asked on January 28, 2021 by chris-steinbeck-bell

0 Asked on January 28, 2021 by ziqi-fan

1 Asked on January 28, 2021 by fady

1 Asked on January 28, 2021 by t-i

convergence divergence examples counterexamples general topology sequences and series

2 Asked on January 28, 2021

2 Asked on January 28, 2021

3 Asked on January 27, 2021 by questmath

1 Asked on January 27, 2021 by user-492177

1 Asked on January 27, 2021 by user21

0 Asked on January 27, 2021 by rivers-mcforge

collatz conjecture convergence divergence elementary number theory prime numbers recursion

1 Asked on January 27, 2021 by almhz

2 Asked on January 27, 2021 by sicmath

Get help from others!

Recent Answers

- Peter Machado on Why fry rice before boiling?
- Lex on Does Google Analytics track 404 page responses as valid page views?
- haakon.io on Why fry rice before boiling?
- Joshua Engel on Why fry rice before boiling?
- Jon Church on Why fry rice before boiling?

Recent Questions

- How Do I Get The Ifruit App Off Of Gta 5 / Grand Theft Auto 5
- Iv’e designed a space elevator using a series of lasers. do you know anybody i could submit the designs too that could manufacture the concept and put it to use
- Need help finding a book. Female OP protagonist, magic
- Why is the WWF pending games (“Your turn”) area replaced w/ a column of “Bonus & Reward”gift boxes?
- Does Google Analytics track 404 page responses as valid page views?

© 2023 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP