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Sokoban is quite interesting. I am not sure that there is a "Standard" set of levels though.
Have you played "Baba is You"?
In "Elementary Real and Complex Analysis" by Shilov, numbers of the form 2n are defined as even, and 2n+1 as odd. These definitions arise early in the axiom list, so you could certainly say they are axioms.
Your proof is therefore enough. I would add a little:
Let n be any integer. Then n + 1 is the next integer, so n and n+1 are consecutive.
Adding them gives n + n + 1 = 2n + 1 which is odd from the definition of an odd number.
Bob
I agree with Bob here: the words are necessary; without the words, you have a soup of algebraic expressions
darn that's a cool watch
What do you do on cloudy days?
No, I am not Christian.
Sorry to ask, but are you American?
I hope you are enjoying it. Which programming language are you learning?
I admire your effort to set up a working sundial.
For now, I will stick to my primitive ways of using a battery-powered wrist-watch.
From where I am, the last two years of high school math were definitely more challenging. The real tragedy was that you had to be prepared to be able to do a lot of different problems very quickly in the exam.
The tenth grade math was alright, though.
Did you do anything fun during the summer?
Okay!
It is great to see that you are sticking around and helping people on the forum
How is everything going?
I come back to this forum once in a while, and post some random things. It is a great place to hang out on the internet. Especially so if we are talking about the platforms that are not owned by for-profit corporations
Hey, I have lived in Houston too, for the last 5 years.
I am not a tenth grader, but when I was a tenth grader, I was here. Welcome to the forum.
I think it is an interesting concept. I am just skeptical that a big franchise with so many books will actually write good books for all of those topics
Yes. I'll ask my PA, Matilda, to send you an email.
Bob
You have a personal assistant?
The Steam Deck is a gaming handheld, like the Nintendo Switch. I really like it. This is not because of the games I can play on it.
I like it because it doesn't try to curtail user agency, because it uses Linux
I wrote a blog post about this: https://isomorphism.xyz/blog/2024/steam-deck/
I don't really recommend taking information from AI agents seriously. Wikipedia, books, blogs and static websites are a much better source.
Yes, the concept of Factorial is related to counting. But for certain purposes, it makes sense to extend it to real numbers (decimal numbers, as you call them). The Gamma Function is one such function.
I can't seem to load smiles.com
Does it work for you?
Today 666bro sent me an email asking
I'm intended to learn mathematical softwares especially open source one which is the good one to start with?
Here is what I wrote back:
Here are some tools you could try learning. They are related to mathematics but they are very very different things.
(1) R for statistics: This is a useful tool for making plots and graphs for your data.
(2) Sage for computer algebra: This is a swiss army knife tool - equivalent to mathematica. Tutorial should give you some idea of what you can do with it.
(3) Lean for verified proofs: In Lean, you can write the proof of a theorem and get the computer to check that your proof is correct. Check out Learning Lean and especially the "Natural Numbers Game".
(4) Z3: Z3 is a general purpose reasoning tool that can be used to solve puzzles or check large scale formulas written in a certain language. Tutorial
Do lay-people really teach themselves mathematics using Bourbaki books?
What is NCTM KenKen? I couldn't find it by a google search
Yes, Quora is very interesting. I spend a lot of time on Quora.
Have you heard of Nebula? It is a website where creators upload youtube style videos. However, it is not open to all like youtube, only invited creators post content.
Here is a list I have:
1. Notion
2. Slowly
3. What 3 Words
What have you found?
Hello all;
Please check out my Tic Tac Toe Tutorial with Haskell.
I also have 7 lecture crash course: https://agnishom.github.io/haskell-21/
That is interesing. I am glad that the administrators have a growth mentality and are trying to learn new things. This certainly makes for a great morale in this community.
Hi,
I have been questioning for ages but can it be possible for an Administrater to ask help from the Members and the Real Members? I have been reading all the posts but not even one administrater has even asked for help.
That is an interesting observation. I guess this either means that the administrators are not really hunting problems in the wild, or that they do not believe that members of this forum will be able to help them in what they need help with.
There are an infinitude of pairs (x,y,z). How can we brute force all of them?