Mathematics Asked by simey on September 19, 2020

I’m struggling to figure out how to prove that the set of all finite subsets of $mathbb{R}_+$ is countable. I thought that it wasn’t but a TA told me it was and I need to prove why it’s countable. I don’t even know how to start this proof.

If it helps, I solved this problem with $mathbb{Z}_+$ by saying when writing down first several subsets of $mathbb{Z}_+$, you can clearly see a pattern that can be enumerated.

It is false. That set contains all the singletons from $R^+$ which is itself uncountable. So the set must be uncountable. Also, if $R^+$ is replaced by $Z^+$ it is still false as the power set of $Z^+$ is still uncountable !

Answered by The73SuperBug on September 19, 2020

Get help from others!

Recent Questions

- How can I transform graph image into a tikzpicture LaTeX code?
- 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?

Recent Answers

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

© 2024 TransWikia.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP