4 sqrt(3)
let's talk about Bridgerton tea, my ask is open

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@sqrt-48
4 sqrt(3)

Anya is live and ready to show you everything. Watch her strip, dance, and perform exclusive shows just for you. Interact in real-time and make your fantasies come true.
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Reblog to give prev a notification.
omg this one actually works
Yes, it does.
Seems implausible if you ask me
you can also like the post for a similar, but noticeably different notification
bestowing upon thee two notifications
Hello there prev this is notification Iโll just let myself into your inbox
Hello. Got rid of my introduction post because someone did remind me of common sense and being safe on the internet and not volunteering personal information. I am slightly sad because I did like my intro.
I think I'll go back to being a mysterious lizard on the internet, I suppose.
Hello. I am me. I mostly post about Mathematics and the Cosmere, but as this is my main blog, also any other random shiny posts I see and wish to reblog.
I have 13 sideblogs! My three favourites at the moment are @the-ordinals, @the-first-gem, and @nightblood-type-iv-entity, so check them out!
No Ruin? You'll hurt its feelings. /silly
I mean, someone else is Ruin. That one isn't one of mine. (Should we maybe make a roll (role?) call of Cosmere rp blogs?)
I thought you were @the-voice-of-god
In the interest of role call for rp accounts I'm:
@osofficial
@uncanny-library-official
and one more to come once I figure out who, make the drawing, and build the blog
I am:
@ati-official
@give-me-your-passion
@the-survivor-of-hathsin-official
@ironeyes-twice-over
@the-cooler-venture
Ooh. One, I apparently hadn't followed Rayse. Two, I didn't realise you were the Survivor of Hathsin.
I suppose I count as a sideblog although Tumblr doesn't know who else I am
Enh Enh Enh. We thrive on anonymity.
School messes with ur brain. Why am I excited that my new calculator has a fraction button?
Because math is fun!
@anremithrl this is accurate
Math is fun!
Math is fun!
We should start a chain of this to blow up OPs notifications.
Math is fun!
I am fun!
M A T H I S F U N we have 9 letters so we have 9! combinations 9! is just bigass nine you can write 9! as
NINE
that's pretty big nine
nine is actually hands down the best number
Nine is cool but six
Six is better
9 devides only by 3, 1 and 9 (sorry idk if it's a good translation)
But six
6 devides by 1, 2,3 and 6
It's just better
I like 256
*casts โ-1*
โค
6 is divided by primes:
2,3,6
Up to associates.
Taking all the combinations yields
1,2,3,6
For divisors of six, up to associates.
Permuting by the set of units, and taking all their combinations, gives:
1,2,3,6,-1,-2,-3,-6.
*spell is cast*
*vwoooop*
โค[i]/(iยฒ+1)
Still a UFD!
6 now has prime factorisation:
1+i, 1-i, 3
Leading to divisors:
1, 1+i, 1-i, 3, 2, 3+3i, 3-3i, 6
Up to associates. Permuting by the set of units: 1,i,-1,-i we can tell that 6 is now divided by:
1, 1+i, 1-i, 3, 2, 3+3i, 3-3i, 6, i, -1+i, 3i, 2i, -3+3i, 6i, -1-i, -3, -2, -3-3i, -6, -i, -3i, -2i, -6i
Also, @olgierd-rudy-103, 6 is perfect.
Six is perfect!
Have you considered zero.
My url used to be zero-is-even before I acquired the cosmere as a hyperfixation and/or special interest.
49 is superior because squares are good and seven is good
yes, 49 is my favorite square, but NINE!!!!!!! Nine multiplies so nicely!
Yes! Nine! I loved nine for this in elementary school!
09 then you add one on the left and subtract one on the right and you fucking get 18. Repeat 27. 36, 45, etc.
And if you take the number you're multiplying nine with you just have to subtract one and then count up to the next ten thingy!
in like the second grade I spent ten minutes realizing the times nine table on my own and it was life changing
Things i have seen so far:
-People like numbers that are 1 less than the base they are written in
-People like perfect numbers
Conclusion:
base 7 or 29 or 497 are the best bases (others would be too big)
I love how horrible this is. Who wants to work in base seven?
Base 7
I do!
No. Why?
Hi
Wait, you're like... really close to me, numerically.
Approx, 1/14 away.. (harmonic series) [but if you're asking the guy running this i's more like 42 away]
So why should we choose you as a base?
School messes with ur brain. Why am I excited that my new calculator has a fraction button?
Because math is fun!
@anremithrl this is accurate
Math is fun!
Math is fun!
We should start a chain of this to blow up OPs notifications.
Math is fun!
I am fun!
M A T H I S F U N we have 9 letters so we have 9! combinations 9! is just bigass nine you can write 9! as
NINE
that's pretty big nine
nine is actually hands down the best number
Nine is cool but six
Six is better
9 devides only by 3, 1 and 9 (sorry idk if it's a good translation)
But six
6 devides by 1, 2,3 and 6
It's just better
I like 256
*casts โ-1*
โค
6 is divided by primes:
2,3,6
Up to associates.
Taking all the combinations yields
1,2,3,6
For divisors of six, up to associates.
Permuting by the set of units, and taking all their combinations, gives:
1,2,3,6,-1,-2,-3,-6.
*spell is cast*
*vwoooop*
โค[i]/(iยฒ+1)
Still a UFD!
6 now has prime factorisation:
1+i, 1-i, 3
Leading to divisors:
1, 1+i, 1-i, 3, 2, 3+3i, 3-3i, 6
Up to associates. Permuting by the set of units: 1,i,-1,-i we can tell that 6 is now divided by:
1, 1+i, 1-i, 3, 2, 3+3i, 3-3i, 6, i, -1+i, 3i, 2i, -3+3i, 6i, -1-i, -3, -2, -3-3i, -6, -i, -3i, -2i, -6i
Also, @olgierd-rudy-103, 6 is perfect.
Six is perfect!
Have you considered zero.
My url used to be zero-is-even before I acquired the cosmere as a hyperfixation and/or special interest.
49 is superior because squares are good and seven is good
yes, 49 is my favorite square, but NINE!!!!!!! Nine multiplies so nicely!
Yes! Nine! I loved nine for this in elementary school!
09 then you add one on the left and subtract one on the right and you fucking get 18. Repeat 27. 36, 45, etc.
And if you take the number you're multiplying nine with you just have to subtract one and then count up to the next ten thingy!
in like the second grade I spent ten minutes realizing the times nine table on my own and it was life changing
Things i have seen so far:
-People like numbers that are 1 less than the base they are written in
-People like perfect numbers
Conclusion:
base 7 or 29 or 497 are the best bases (others would be too big)
I love how horrible this is. Who wants to work in base seven?
Base 7
I do!
No. Why?
Hi
Wait, you're like... really close to me, numerically.

Anya is live and ready to show you everything. Watch her strip, dance, and perform exclusive shows just for you. Interact in real-time and make your fantasies come true.
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I think a problem with (but also the amazing thing about) bounded arithmetic is that it is soooo interdisciplinary. Like you need to know a good amount of both proof theory and model theory but also a good amount of theory of computation and algorithms to even begin to understand why people do what they do and why are the problems interesting. And then you're going to borrow methods from basically every algebra-aligned field to figure it out.
And we know nothing. Even though the basic open questions can be formulated somewhat clearly, the things you're going to be working on (especially at a graduate level) are like 5 levels down the rabbit hole and even something like conditional unprovability of one little thing is a state-of-the-art result with huge implications because we don't know how to do anything.
Good resources for learning?
School messes with ur brain. Why am I excited that my new calculator has a fraction button?
Because math is fun!
@anremithrl this is accurate
Math is fun!
Math is fun!
We should start a chain of this to blow up OPs notifications.
Math is fun!
I am fun!
M A T H I S F U N we have 9 letters so we have 9! combinations 9! is just bigass nine you can write 9! as
NINE
that's pretty big nine
nine is actually hands down the best number
Nine is cool but six
Six is better
9 devides only by 3, 1 and 9 (sorry idk if it's a good translation)
But six
6 devides by 1, 2,3 and 6
It's just better
I like 256
*casts โ-1*
โค
6 is divided by primes:
2,3,6
Up to associates.
Taking all the combinations yields
1,2,3,6
For divisors of six, up to associates.
Permuting by the set of units, and taking all their combinations, gives:
1,2,3,6,-1,-2,-3,-6.
*spell is cast*
*vwoooop*
โค[i]/(iยฒ+1)
Still a UFD!
6 now has prime factorisation:
1+i, 1-i, 3
Leading to divisors:
1, 1+i, 1-i, 3, 2, 3+3i, 3-3i, 6
Up to associates. Permuting by the set of units: 1,i,-1,-i we can tell that 6 is now divided by:
1, 1+i, 1-i, 3, 2, 3+3i, 3-3i, 6, i, -1+i, 3i, 2i, -3+3i, 6i, -1-i, -3, -2, -3-3i, -6, -i, -3i, -2i, -6i
Also, @olgierd-rudy-103, 6 is perfect.
Six is perfect!
Have you considered zero.
My url used to be zero-is-even before I acquired the cosmere as a hyperfixation and/or special interest.
49 is superior because squares are good and seven is good
yes, 49 is my favorite square, but NINE!!!!!!! Nine multiplies so nicely!
Yes! Nine! I loved nine for this in elementary school!
09 then you add one on the left and subtract one on the right and you fucking get 18. Repeat 27. 36, 45, etc.
And if you take the number you're multiplying nine with you just have to subtract one and then count up to the next ten thingy!
in like the second grade I spent ten minutes realizing the times nine table on my own and it was life changing
Things i have seen so far:
-People like numbers that are 1 less than the base they are written in
-People like perfect numbers
Conclusion:
base 7 or 29 or 497 are the best bases (others would be too big)
I love how horrible this is. Who wants to work in base seven?
Base 7
I do!
No. Why?
Okay. What math do you like the best?
Algebra 1
Algebra 2
Geometry
Trigonometry
Calculus
Pre algebra
Accounting
A few more options
Abstract Algebra
Analysis
Topology
Logic
Category Theory
Number Theory
Geometry
Dynamics
Graph Theory
Ergodic Theory
Representation Theory
Probability Theory
I ran out of space for options.
I am simple (I am not on the complex plane), I see math blog and I press the follow button
No, no, simple means you're a group with no normal proper nontrivial subgroups.
No. Simple is a graph that has no loops.
Proof Techniques (Informal)
We do a lot of proofs in mathematics. So it's relevant to have some general intuition for the informal notions of how we talk about proofs, so that there is intuition that more precise notions can crystallise around.
While there are more developed and formalised systems of proofs capable of proving things more clearly and precisely that are able to be studied in their own right, the goal here is to introduce some basic ideas and intuitions for proofs. These don't tend to be used individually, but mixed and matched and represent a more general notion of things.
Constructive Proofs
These are their own whole rabbit hole on their own, and there are whole branches of math devoted to this. Most notably, type theory.
One simple and intuitive way you might want to try to prove something is to just provide an example of the thing.
Let's say you want to prove that 4 is even. Well a number is even if it is a multiple of 2. So if we provide "2*2=4", then we have a proof that 4 is even.
"Any even number plus 2 is even."
So it takes an even number x. Since we know that x is even, we have an element y such that 2y=x.
2y+2=x+2
2(y+1)=x+2
Therefore, we found our candidate. If x is a number, and it has a proof y that it is even, x+2 has a proof that it is even, namely y+1.
How can you prove that there exists a number such that the sum of its factors equals its squares? By providing a number: 6, and checking the computation.
This kind of proof is called a Constructive Proof. Proof by construction can be surprisingly strong at times. But it has a handful of large weaknesses.
We often call the provided proof in a constructive proof a witness.
For example: Can you proved a witness to the claim that 64 is a perfect square?
Proof by Exhaustion
This is just a proof where you brute force the thing. For example, you can prove that every number less than ten thousand that ends in 0 is a multiple of ten by manually checking each one. That's a waste of time in that specific case but technically possible.
If you have reduced something to a finite list of things, you can just try all of them. Very often people don't manually do proof by exhaustion, but rather have a computer check a bunch of cases. An example of an exhaustion step was how all the base cases were checked for the four-colouring problem.
There isn't much to say on this one.
Proof by Cases
This is kind of the same thing as proof by exhaustion, where you prove it when one thing is true, and again if it was false. I have listed it separately because it's a special case of proof by exhaustion. You can nest these to get more cases, and thus do arbitrary proof by exhaustion. The vibe is sort of different, though.
An example is the proof that nยฒ+n is always even. There are two cases, n is even, and n is odd. If n is even, it is 2m, and thus nยฒ+n=4mยฒ+2m=2(2mยฒ+m)
And if it is not even, then it is 2m+1, and hence
nยฒ+n=4mยฒ+4m+1 + 2m+ 1= 4mยฒ+6m+2=2(2mยฒ+3m+1)
And hence is even.
Proof by Assumption
Let's say you want to prove that whenever A is true, B is also true. In that case you begin by assuming A, and then you can see what else is true.
For example, if a divides k, then a divides bk for every b.
First you assume that a divides k. That means there is some n such that na=k
And then that means that for every b such:
bna=bk
Hence an also divides bk.
Proof by Contrapositive
This is a special case of proof by assumption. Instead of assuming the premise, you assume the end goal is false, and show the premise must be false.
For example, if nยฒ is even, then n is even.
If n is not even then n=2m+1 for some integer m. And thus nยฒ=4mยฒ+4m+1, which is an even number plus one. nยฒ=2(2mยฒ+2m)+1 hence if n is not even, nยฒ is not even.
Therefore, by contrapositive, nยฒ is even means that n is even.
Proof by Contradiction
Proof by contradiction is where you begin by assuming that something is not true, and you show that that doesn't make any sense.
For example, โ2 is irrational:
Let's begin by assuming the opposite, that it is rational. In that case
a/b=โ2
And thus there is some smallest pair a and b such that
aยฒ/bยฒ=2
Where this is as simplified as you can make it. But the goal is to show it can still be simplified, because it doesn't make sense if either number is odd.
Or:
aยฒ=2bยฒ
This means aยฒ is even.
And an odd number squared is odd, so aยฒ being even implies a is even. Let's call hald of a as n.
Notably, this means aยฒ=(2n)ยฒ=4nยฒ, hence
4nยฒ=2bยฒ
And thus
2nยฒ=bยฒ
But that means b is even, or equal to some 2m.
But if a/b is made of two even numbers, then n/m is the same as a/b. n/m is thus a more simplified version of a/b. Which contradicts where we said a/b was the most simplified version. Therefore, there is no such rational a/b.
Hence the square root of 2 is irrational.
Inductive Proof
Proof by induction! This is where I come in! (Ordinals are the structure that induction works on.)
This is where you prove something by showing it is true for some smallest case, and then if it is true for all the smaller cases, then it must be true for the next case.
For example, every natural number is either 2m or 2m+1.
Base case: 0
This follows by construction by the witness m=0
Inductive step: n+1
Now we prove it for any n+1.
If you already know it's true for every number less than n+1, then that means you know n is equal to some 2k or some 2k+1.
Proof by case:
Case: n=2k
Then you have the witness m=k, that shows n+1 equals 2m+1.
Case: n=2k+1
n+1=2k+1+1=2k+2
And thus the witness m=k+1 shows that n+1=2m for some m.
Formal Proof
This is doing a formalised proof in a proof system. Most formal proofs need no instances of natural human languages, since they use their own new languages that are easier to check and verify. This is when you start being super careful. You can justify all the techniques I've introduced above in most formal systems.
And some bonus proof techniques visible here, which were part of the original post I thought but apparently not?
There's also proof by intimidation. Proof left as an exercise to the reader/reviewer/grader.

Anya is live and ready to show you everything. Watch her strip, dance, and perform exclusive shows just for you. Interact in real-time and make your fantasies come true.
Free to watch โข No registration required โข HD streaming
Please-do-it?
donโt-do-it-courageous-person
Letโs see
@imbalance-the-order-demon
@singularity-the-peace-mortal
Thereโs surely more ways
An-artist-with-a-good-life
Idfk
There is actually a blog for it like theseriousgal or something
ignore-hamster-singular-timeline
Tik2
Mordor
Heap of function
-โ48
Interesting math fact of the day #156:
Either p is a square mod q and q is a square mod p or neither is true.
7 is a square mod 3 but 3 isn't a square mod 7
Stupid search engine being stupidly stupid. Changing it rn
that ain't how tumblr works buddy. your mistake still exists in all the reblogs from before the edit
I know, but this post will be forgotten in a week like all the others
do you. really think so.
๐
putting this into the queueueueue
no not the q
This will.keep circulating dw
Awawa hey wait wo are you
@sqrt-48 get in here as well
ayy lmao
hi ther
@sqrt-74 join in
why would I betray my brother
Are we not your other brothers?
the traitor brothers
It is no treason, second root of the sum of my square and the square of 5 and the square of 1, is the very one you defend.
Take the difference between my square and his own, and coupled with his own square you shall see that it forms a contradiction to his very words.
It is the duty of us, as his friends, to, in true brotherly fashion, never let this become forgotten.
You do not betray him. This is our duty.
youโre math is wrong. why? take 93 times your enemyโs square and subtract 140 of yours. youโll get what me and your mother, positive 73, did last night. brothers stick together, neighbors can fight. now, if youโll excuse me, i have a post to forget.
Forget away brother.
Still forgetting it? Enh Enh Enh!
tumblr isnt giving me enough dopamine cmonnnn sluts look at my posts. say words under my posts
okay we all know what to do right?
We have to say "words under my posts".
reblog this if you want others to say words under your posts
No no. That's "words under your posts"... or potentially "words" under posts, not "words under my posts". You've misunderstood!
sure, but words under posts include "words under my posts". I've just generalised
No! That's under standing. Where you take a stand for yourself, but you do it under! I was talking about understanding! Which is the same thing but you take the space and swallow it. Which is a lot like swallowing words, except you don't have to swallow any words.
i can at most wallow swords, is that enough?
I think it is! You'll need to use the sword to cut out the space in under standing, and shred it to ribbons.
Oh, but can you reach it from all the way down here?
i think i can, but i think i'll have to stand on one of the swords
Here! Have some armour for your feet so they don't get poked or cut by the sword!
yay! thanks!
words under my posts
words under my posts
words under my posts
words under my posts
words under my posts
Make some math art.
Make sure to capture my good side!
All your sides are beautiful.
@always-calculusting
A few years ago while trying to find ways to commit suicide as painlessly as possible, I came across a PDF of Dr. Paul Quinnett's The Forever Decision. Thinking it might go into actual methods of suicide (I read an article once that actually did that and was trying to find it again) I started to read it, and I think I only got about two pages in before I was crying too much to actually see the words.
I downloaded the PDF to my hard drive and I open it again whenever I'm feeling too suicidal to do much else, but not enough to start booking a ride to the hospital. And every time without fail I only go up to a few pages before backing off and choosing to live another day just because suicide suddenly seems even more unbearable than whatever the hell upset me in the first place.
All the book really does is [I'm pulling a summary from GoodReads here as, again, I've read no more than 5 pages] "discusses the social aspects of suicide, the right to die, anger, loneliness, depression, stress, hopelessness, drug and alcohol abuse, the consequences of a suicide attempt, and how to get help."
But it also starts with the author kindly asking the reader to complete the book before going through with anything, and for some reason I'm compelled to really just try to read it all before finalizing everything. Despite not yet completing it (hopefully never will) I think I can safely say it's saved my life at least a few times now.
It's intentionally legal to copy and redistribute this book to keep it as accessible as possible, and it's very easy to find, but here's a link for it anyways.

Anya is live and ready to show you everything. Watch her strip, dance, and perform exclusive shows just for you. Interact in real-time and make your fantasies come true.
Free to watch โข No registration required โข HD streaming
Interesting math fact of the day #302:
No integer is coprime to exactly 14 distinct others
well yeah every integer is coprime to infinitely many distinct others
I forgot the Lea
let
โค
what is the full statement you wanted to say
No integer has 14 numbers less than it coprime to itself
What about 73?
exactly 14
Wait, you have an evil twin?
no heโs the nice twin i forgot who the evil twin was itโs a long story
It was probably @sqrt-74 or @sqrt-48 or something.
Probably.
I have historically posted my annual mathblr roll call in late April, but I think it makes more sense to do it at the beginning of the year so it's clear which post is current. Accordingly, I now call the
๐งฎ ๐๐๐๐ ๐๐ธ๐โ๐น๐โ โ๐๐๐ โ๐ธ๐๐ ๐งฎ
Reblog/reply if you are a mathblr and/or mathblr adjacent. And tag the other (at least semi active) mathblrs & adjacents you know of!
"What counts as mathblr? Do I count?" If you want to! Math shitposters! Math academia aesthetic blogs! Math studyblrs! Math related gimmick blogs! Unthemed blogs owned by people who happen to be math fans! I want them all! I'm happy to see CS, stats, physics, and other math-adjacent folks too if they like hanging out with the math crowd!
Bonus: link to the LCM- Least Common Mathblr discord server. Come hang out!
https://discord.gg/q4nzuEqgFv
Joining in the reblogging crewโฆ as I make this page chiller/become more active :)