What is a monoid? |  

This is the most clear and intuitive explanation I've found so far. Thanks!

This is absolutely great. Thank you for the great content and please PLEASE 🙏 do other videos

Thank you for the amazing explanation!

Currently, I still don't quite get it but you've explained it the best of all videos I've seen and I have a slight understanding. Thank you for taking the time to help others in sharing your wonderful gift(s) :)

You have an amazing collection of books, Can you do tour of your library? The pattern that evolves out from the choice of books shows your desire to unearth the whole meaning of life with mathematics.

Amazing! I knew monoids, but finally I really understand them. I know it's a longer way and you are doing more 'basic' videos for now (which I am looking forward to), but I hope you will make a similar video for monads sometime.

Very interesting and clearly presented. Thank you.

You should make more of these. Either deeper into Monoids or do some on other structures.

Great video! Would have been even better if you explicitly showed that the neutral element is both left-neutral and right-neutral. :-)

Thanks for the concrete example! I especially liked the antimatter books. I wonder why you can't just express inverses as mere subtraction (taking away books). Probably because if you must subtract, you then lose things like associativity. If you lose associativity, suddenly you can't do things like arbitrary division of computation in the case of distributed networks. I wonder if there is an "associativizer" pattern, that can take such a need (for lack of direct inverses, but need to correct for elements), and shim a level of indirection to regenerate associativity while affording an ability to apply inverses without direct ones. The books may be a good example to think about this more. It may be simply impossible, consequently constraining you to segregate your phases of computation such that you don't "taint" your associative & thus parallelizable computation with non-associative operations. Great stuff! Generated plenty food for thought with just a simple & meaty example.

This is a fantastic explanation!

Great explanation! Reminded me of my discrete math prof Kim Factor

cool! thanks for your insights!

A round of applause for this man!! subscribed to your chanel!

duidelijke uitleg!

Thanks for this! I almost clicked off after you'd given the definition (which is what I came for), but I'm glad I didn't. That was enough to give me the mathematical intuition as a group without inverses, but now I also understand (what I presume is) the programming motivation as the extension of a binary operation.

In older texts, the primary structure was the module, a concept closely related (but not identical) to monoid. I hope to follow more of your videos!!

Something that I’m still confused about is, what exactly is the monoid in this scenario? What I’m asking is, is the operation itself the monoid? Is the monoid a certain set of data? Monoid is a noun, so what kind of thing is a monoid? With dependency injection in OOP, dependency injection refers to the act of passing an instance of an object as a parameter to a method rather than instantiating the object inside the method, thereby separating creation from use. That action is what dependency injection is. I’m clear on what the word monoid refers to.

Bourbaki abolished the term semigroup for taste reason.

good explanation. you also remind me of a high school classmate of mine, are you sure English is your native? (it is very good, I am just curious)

📚Shared this gem to the less-mathematical friends, let’s see how it’ll go!

why books don't simply do that

i own 2 of those six books

Subtract equations is not monoid lol (based on the definitions provided in the video)

Thks & en.wikipedia.org/wiki/Algebra#Groups