Anything Math



05022017, 12:36 AM
(This post was last modified: 05022017 12:45 AM by Kernel Sohcahtoa.)




Anything Math
IMO, at its core, mathematics is a very beautiful and awesome subject; however, I'd like to learn how other people see mathematics and what intrigues them about it. Hence, the purpose of this thread is for members to share anything mathrelated that they find interesting, cool, beautiful, etc.
In order to kickstart this thread, I will post some proofs for even and odd integers. Now, we intuitively know that an integer is even or odd, but, IMO, it is still cool to see how this fits into a broader framework via definitions and proofs. * I'm posting the proofs in spoiler tags, so that people can attempt the proofs for themselves if they wish. Definitions Definition of an even integer: An integer n is even if n=2a for some integer a Definition of an odd integer: An integer n is odd if n=2a+1 for some integer a Prove the following statements 1. If x is even, then x^2 is even Proof 2. If x^2 is even, then x is even Note Proof 3. If x is odd then x^2 is odd Proof 4. If x^2 is odd then x is odd Proof "I'm fearful when I see people substituting fear for reason." Klaatu, from The Day The Earth Stood Still (1951) 

2 users Like Kernel Sohcahtoa's post 
05022017, 12:43 AM




RE: Anything Math
Cantor's diagonalization method is always fun at parties.
#sigh 

4 users Like GirlyMan's post 
05022017, 01:02 AM
(This post was last modified: 05022017 08:32 AM by Kernel Sohcahtoa.)




RE: Anything Math
(05022017 12:43 AM)GirlyMan Wrote: Cantor's diagonalization method is always fun at parties. Agreed. IMO, I found this to be very fascinating and mind boggling when I read about it in the Book of Proof by Richard Hammack. In particular, I remember that Cantor's diagonal method proves that there are no surjective functions from ℕ to ℝ, which means that there are no bijective functions. Consequently, the cardinality of ℕ does not equal the cardinality of ℝ, as ℕ is a countable infinity while ℝ is uncountable; thus, ℕ and ℝ are two different types of infinity. "I'm fearful when I see people substituting fear for reason." Klaatu, from The Day The Earth Stood Still (1951) 

1 user Likes Kernel Sohcahtoa's post 
05022017, 05:31 AM




RE: Anything Math  
2 users Like morondog's post 
05022017, 03:08 PM




RE: Anything Math
(05022017 01:02 AM)Kernel Sohcahtoa Wrote:(05022017 12:43 AM)GirlyMan Wrote: Cantor's diagonalization method is always fun at parties. Or you could just say, whoa look at that, there are more real numbers between 0 and 1 than we can count. Well fuck me sideways, how can that be? #sigh 

1 user Likes GirlyMan's post 
05022017, 03:29 PM




RE: Anything Math
One of my life goals is to understand math.


2 users Like GenesisNemesis's post 
05022017, 03:31 PM




RE: Anything Math
(05022017 03:29 PM)GenesisNemesis Wrote: One of my life goals is to understand math. That is also a goal of mine. I'm still very far from achieving it. Live long and prosper, sir. "I'm fearful when I see people substituting fear for reason." Klaatu, from The Day The Earth Stood Still (1951) 

1 user Likes Kernel Sohcahtoa's post 
05022017, 04:19 PM
(This post was last modified: 05022017 04:29 PM by GirlyMan.)




RE: Anything Math
Not to politicize this thread or anything but to politicize this thread, Cuban/Zuckerberg 2020!
To Live Your Best Life, Do Mathematics #sigh 

2 users Like GirlyMan's post 
05022017, 04:33 PM




RE: Anything Math
(05022017 03:29 PM)GenesisNemesis Wrote: One of my life goals is to understand math. She's a cruel cruel mistress taunting me with PDEs and Lagrangians and homomorphic manifolds and ZFC and .... #sigh 

2 users Like GirlyMan's post 
05022017, 05:01 PM
(This post was last modified: 06022017 07:16 AM by Kernel Sohcahtoa.)




RE: Anything Math
(05022017 04:19 PM)GirlyMan Wrote: Not to politicize this thread or anything but to politicize this thread, Cuban/Zuckerberg 2020! Those were some marvelous words, GirlyMan. Thank you for posting this. Live long and prosper. "I'm fearful when I see people substituting fear for reason." Klaatu, from The Day The Earth Stood Still (1951) 

« Next Oldest  Next Newest »

User(s) browsing this thread: 1 Guest(s)