ITT: Cool shit that you wish somebody had shown you when you were a kid/undergraduate
What's cool about that?
>>7751032
If you can't see the pattern you're retarded.
>>7751200
every number can be bit shifted so as to have a 1 in the lsb?
>>7751200
>impressed by patterns
>>7751022
Wow, 8 multiplied by a number divided by 8 gives you the same number, thanks OP! I've finally found a topic for my paper!
>>7751022
Every even number x can be represented as the product p*y with a prime number p and an even number y<x.
>>7751022
the dankest meme in town: -1/12
>>7751022
It's easy with category theory. Draw horizontal arrows that denote adding some amount.
f:1-->3
where f(x)=x+2
Do this for all elements. Then Each row can be considered a category. Furthermore, your vertical arrows can then be considered as a functor acting on each category. Define
F(x)=x/2
and given f(x)=x+n
F(f)=f'
where f'(x)=x+(n/2).
Now you have a structural argument for why this pattern works.
![37b83e23225570b16dc52d4d07240902[1].jpg](https://i.imgur.com/jqcTVds.jpg "37b83e23225570b16dc52d4d07240902[1]")
x/x = x รท x
It never clicked in my head in highschool.
They worked as two completely different functions in my brain.
>>7751274
>defining trivial functions that add numbers is a "structural argument from category theory"
fuck /sci/ and this meme thread
>>7751022
>If you divide by 2 until all the even number's prime factors of 2 are gone, it'll be odd!!
stupid.
If you look at the prime factorization of any of those numbers, it'll be
[math]
1*2^n
[/math]
or
[math]
3*2^n
[/math]
or
[math]
5*2^n
[/math]
etc.
Nothing exciting or special about this.
>>7751022
Since OP is impressed by meme patterns, let me present something I was playing around with once.
>>7751022
wow if I divide those numbers by 2 if they are even and multply them by 3 and add 1 of they are odd and if I keep repeating that process they all end up at 1. astonishing
>>7751343
Here's a sudoku-like game that has to do with your chart: garamgame.com
>>7751022
Wow, every even number either has an odd factor or it doesn't.
I'm really surprised this didn't win a golden coin.
>>7751236
nope
>>7751357
If 4 divides x, then p=2 y=x/2
If 4 doesn't divide x, x has prime factors including 2, take any one of them but 2 as p and the rest of them as y
I was never introduced to the pascals triangle when I was a kid
Such a shame
>>7751200
>MIND=BLOWN
>U'VE BEEN DOING IT WRONG UR WHOLE LIFE
>I FUCKING LOVE SCIENCE
>ONLY TRUE NERDS WILL GET THIS ONE
I wish someone showed this to me when I was 10.
Calculus was fun.
