A divisibility lattice for the number 60.Â
Mathematics is beautiful. <3
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@functionaldesign
A divisibility lattice for the number 60.Â
Mathematics is beautiful. <3
I have been wondering what this is called for weeks.

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I'm gonna go fucking bezerk
"what change did you make?"
"I software engineered"
"yes but what change did you make?"
"code changes"
"yes... But what code changes"
"uh,, adding... Stuff"
A lovely animation depicting a few partial sums for the Fourier series of a square wave by stacking rectangles.
Mathematics is beautiful. <3
The Jews: pi is three
Other cultures: Iâm pretty sure itâs a little bit mo-.
The Jews: fuck you, pi is three.
Thatâs not how I interpret this text. This is saying that the evidence of G-dâs wonders can be seen in every circle, because a circleâs ratios forever match the proportional circumference that could be measurable by Judah ha-Nasi, relevant in this case not only through his compilation of the mishna but - and this is where divine wonder comes in - for having had three hands. Â
Mathematician 1: this has a solution?
Mathematician 2: what is it
Mathematician 1:
Mathematician 2: wig okay letâs just call it a day then
mathematician 3: weâve proved no solution exists
mathematician 4: wow my lifeâs work has finally paid off with an answer
mathematician 5: I finally have an existence proof!
mathematician 6: I have a constructive proof
mathematician 5:
mathematician 5: ⌠fuck you

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Have you ever wanted to end a proof not with an unfilled square or âQ.E.D.,â but rather with â#get rektâ?
Sometimes we write âQEmfDâ for âQ E motherfucking Dâ.
Too soon?
Any advice on how I can become better at math?
This is all classroom-based because I cannot learn without external motivation, but here are some things that help:
1. Read the textbook before class
2. Take notes but only as a means of remembering what happened in class, not as an end in themselves. The studyblr tag is not a model here
3. Ask questions
4. Go to office hours
5. Do small talk with your professors
6. If itâs been 3 hours and you havenât made any progress, do something else
7. Getting 8 hours of sleep is more important than studying
8. Start early. Do the first problem the day after you get the assignment. The rest will come. Start studying a week in advance, even just 15 minutes
9. Your gut knows more math than you think
10. But donât skip steps
11. Itâs okay to feel like an idiot, it means you probably arenât one
12. Math doesnât have to be your whole identity
13. No one study/note-taking/homework method works all the time. My strategy changes for every class.Â
14. Remember to stop and smell the roses/flirt with the sexy primes/make fun of Pythagoras/fangirl over the FTC/admire adorable proofs/micdrop your QED/etc
Inspired by this twocubesâ post and asked to make an animation of it, I made a gif.

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Basic Linux Commands. Very useful for new Linux users or programmers
youâre forgetting sl! Cant program without Steam Locomotive
yes, you can in fact make a mixed base ânumeral systemâ with unique representations by using factorial bases, like so:
3Ă5! + 4Ă4! + 1Ă3! + 0Ă2! + 1Ă1! + 0Ă0! = 46310
These numbers are called the factoradics. Apparently theyâre nice to enumerate permutations with.
(this post has an error, itâs 463 in base 10. My subscript got taken out by Tumblr :( )
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If this doesnât satisfy you, then (sqrt 2)^(log_2(9)) is a concrete example where irrational^irrational = rational.
Almost all irrational numbers can *only* achieve rational powers using irrational exponents
The set of algebraic irrationals which could achieve rational powers using irrational exponents form a subset of the countable set of algebraic numbers, hence has (Lebesgue) measure zero.
Since transcendental^rational can never be rational, and transcendentals numbers are irrational but not algebraic, one can now say that almost everywhere irrational numbers can never achieve a rational power using rational exponents.
But since for any transcendental number T and any rational number R we have T^{log_TÂŽ} = R, and log_TÂŽ is irrational, it can indeed be concluded that almost everywhere, irrational numbers can only achieve rational powers via irrational exponents.
âAlmost everywhereâ being necessary because there are examples in each case for irrational/rational bases to an irrational/rational exponent giving either an irrational or rational answer.
An obvious irrational that can achieve a rational power by a rational exponent being (sqrt2)^2 = 2.
Say what you will about Java, but javadocs is (are?) a great tool, and more tools like it should be supported by language developers and communities.
As far as I can tell from the spec, `int main()` and `int main(int, char*[])` are both valid ways to declare a main function.
Indeed so it is (I went and looked it up because it started bothering me that I didnât know)
Iâm gonna come clean here and admit that when I said âfrom the specâ, I actually mean âfrom Stack Overflow answers citing the specâ, because Iâve never actually read the C++ spec in my life.

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Hottest take: â â â¤^+ â {2} ⪠{0}
Fuck the number 2
Primes are so much better in this set
THEYâRE. ALL ODD.
Well now you have even numbers that are not composite.
The best part is âevenâ is typically defined as âa multiple of 2â and not âthe stuff that comes between odd numbersâ so âevenâ may not even exist here.
Theyâre just extra primes?
The numbers of the form n+n (not 2n, that string is meaningless) dont necessarily generate a prime ideal, but they also might not be factorable. For instance, 6 is not composite as you cannot factor it (3 times what?) However 24 = 6*4, but 24 can be factored to 8*3, neither of which have 6 has a factor. You lose the "every number is either prime or composite" when you poke holes in the integers like this.
Hottest take: â â â¤^+ â {2} ⪠{0}
Fuck the number 2
Primes are so much better in this set
THEYâRE. ALL ODD.
Well now you have even numbers that are not composite.