A podcast I listen to, "A Problem Squared" (ep. 146), recently answered this question and I'm trying to see if I understand it correctly.

Assumption 1:

0.0499999.... = 0.05.

Assumption 2:

If a number is rounded to the nearest place value, you add 1 to the nth place to be rounded off if the digit to the right is 5 to 9, you truncate if 0-4.

Therefore

0.449999 = 0.45

Rounded to the nearest tenths, it is equal to 0.5.

Is this correct?

Thanks!

I made this question in school

Question is simple. Just finding the red angle
ABCDE is a right pentagon and EFGD, CIHD are squares.

I am finding a solution without computing and approximation.

I'm holding this for over a month please help me

I've tried using congruence and similarity and none helped

Let's suppose I play a fair game of Russian roulette.

We only play 1 round, if the 6-shot gun doesn't fire for me nor my opponent the game is a tie.

After a coin toss it is decideded I play second. The barrel is rolled, the bullet has an equal probability to be in the first or second slot, both at 1/6.

My opponent plays and lives, it's now my turn.

May I request the barrel to be rolled again or would it make the game unfair ?

I'm well aware 'deepest' is a subjective attribute. However, for all intents and purposes, let's consider 'the deepest proof' to maximally satisfy the following:

1. The proof was so profound that mathematicians no longer thought about the subject the same way they did before.
2. The techniques or ideas introduced in the proof could not have been anticipated from the statement alone (the proof itself is irreducible).

P.S. I'm open to your definitions of 'deepest'!

I feel everyone knows the answer to the riddle, “You walk one mile south, one mile west, and one mile north. You end up exactly where you started. Where are you?” The answer is the poles of the Earth which is an interesting way to get thinking about non-Euclidean geometry.

I was wondering, if you assume that Earth is a perfect sphere, why would this answer not be true at any point on the Earth’s surface and not specifically have to be the poles?

In Buddhism there is a number I have heard quite often and have done some calculations about it. It's called Athinchay Which means inconceivable/uncountable But well. That got me curious,so I did some calculations, What I wanted to see was How big was a number that states, 20 Athinchay and 100000 worlds. And I thought well 20 uncountable and 100000 worlds So possibly,100020 times the age of our planet earth.i was absolutely wrong. Well the math doesn't work that ways. Though true definitions can be debated of what Athinchay is in numbers. I have only seen one in mathematics, One Athinchay=1×10¹⁴⁰,so I calculated. That will technically means It's 1×10¹⁴⁰+100000 and each number will represent the age of the world. The 1×10¹⁴⁰ is so big 100000 worlds just doesn't matter anymore. Earth is approximately 4.54 billion years old. So doing the math it will be, 4540000000 × (1×10¹⁴⁰+10000). Which is equal to 4.54e+149 or 4.54 × 10¹⁴⁹. This is just one Athinchay not 20. So that is how big and long the number is.Well one factor. We are looking at the age of the world via scientific age. But Buddhism states the age of each world to be a bit different. I mean in science and in this calculations we are only counting hold old it was since birth to now,that doesn't include death, we can but. I wanted to also calculate the age via how Buddhism describes how long a world is.

And please understand, The inconceivable uncountable number I was left with. Imagine a person who is 100 years old. No. 100×10¹⁴⁰ years old.100 Athinchay years old.every 100 year,we reduce 1 year of that 100 Athinchay years untill the number arrived at 10. This is called "Era of decrease / Eon of decline" Then we go back up, every 100 years we add one to the number until it's back to 100×10¹⁴⁰years old. This is called "Era of increase / Eon of ascension" Both aeons combined we get anantra eon. 64 anantra eons are equal to one Athinchaya eon. Four Athinchaya eons is equal to one world. Now we go back it's 20 Athinchay and 100000 worlds. So I have lay out the lines and I hope someone do the calculations as well and see it. I can do the calculations and I have done the calculations but the problem I'm stuck is not the answer but the conceiving/imagining/understanding it. Comparing it to the age of universe.and universe seems like a baby. (Remember one Athinchay=1×10¹⁴⁰ is the best closest we have, and is not canonically correct by any Buddhist understanding,the most interpreted it was I use it here,the true number of or for Athinchay is still not really know, just like the word, it's meant to be uncountable, inconceivable in anyway possible,yet still finite, it's something so big that it no longers matter) So I am thinking if I tell people about this maybe some will be interested in this math and try to compare to something.

I'm working through the Book of Proof.

Exercise 1.4 asks that we write listed sets by listing their elements between braces.

The set for #11 is { X ∈ P({1,2,3}) : |X| ≤ 1 }

My answer was { ∅, {1}, {2}, {3} }

But the textbook's answer is { ∅, {∅}, {{1}}, {{2}}, {{3}}, {{1,2}}, {{1,3}}, {{2,3}}, {{1,2,3}} }

It seems to me this would be correct for { X ∈ P(P({1,2,3})) : |X| ≤ 1 }, but not { X ∈ P({1,2,3}) : |X| ≤ 1 }

Thoughts?

I just got out of highschool and I am interested in how to formally write a mathematical solution. This is a problem I tried to solve and I want to ask a few questions:

1. Is my solution valid and rigorous? Let me know what my mistakes are

2. Is my way of writing the solution formal enough? What words, phrases, symbols, or anything, can make the tone more formal?

3. What can I do to improve my ability to write solutions/proofs formally?

Bonjour. Je suis élève en première qui aime bien faire des exercices hors-programme. Voici mon premier exercice (que j'ai trouvé sur le Web) et ma résolution, où il faut faire une récurrence forte.

Je me demande si j'ai bien redigé? (Il m'a pris environ 35 minutes de réflexion. J'espère m'améliorer.)

J'apprécierais tous vos remarques et conseils.

okay so on the top of the first image is the original problem, where I'm supposed to find the zeros of f composed of g. I've found that f(g(x)) is (x^2-10)^3 + (x^2-10)^2 - 100(x^2 -10) - 10 which after expanding the binomial and trinomial and then simplifying comes out to x^6-29x^4 -180x^2 and I confidently understand how we got there. then in step 7 it tells me to find the zeros by solving for (f(g(x))=0, and we see it sets up x^6-29x^4+180^2=0, then it says to start by factoring out x^2 which makes it x^2(x^4-29x^2+180)=0. I understand the process here like I get how we factored that out I just don't know why we're doing that, like Idk why I couldn't have just left it as is, but anyway I get the process of that step so whatever. Then we move to step 8 where it says to "set each factor equal to zero. solve for x" and I just straight up don't understand the expressions beneath that, like first off why are we setting both x^2 equal to 0 and x also equal to 0? and next to each of them it says "or [expression]" which is where I'm really lost. where did x^4-29^4+180=0 come from?? in the previous step 29x has the exponent 4 BEFORE we factored out x^2, but now with x^2 on the outside of the parenthesis how is the 29x on the inside to the fourth power instead of squared? also both expressions next to "x^2=0" and "x=0" are the exact same. like i followed everything clearly up until step 7 and 8. 8 I'm entirely lost on, I've tried solving it on my own, I've tried googling tutorials, I've asked my friends, i'm still lost.
And yes this is an example problem and yes it does technically give me the correct answer at the end of these steps but I need to understand how we get there so I can do it myself to solve my actual homework problem. I've done composite functions before without trouble, but this is my first time encountering a composite function that's asking me to fine the zeros.
Can anyone break down step 7 and 8 for me step by step to help me understand what the hell is going on here?? any help would be greatly appreciated. Last image is just me showing my work of correctly following everything up to step 7.

And suggest videos/tutorials, please.

I do pop-up books, and I have a tutorial I really want to follow. But the tutorial's shape and my desired is not the same. For one, the tutorial is based on a square; I need a thinner rectangle to fit into a notebook. So my question is, what's it called when you scale something up or down, and what's it called when you change its shape in addition to scaling it up or down? The problem with pop-up books is that you have to keep some of the 'gears' the same while changing the areas for others. While retaining the same functions.

PLEASE suggest tutorials for this type of math

Hi, am a high schooler not a mathematician. Just to let you people know that my thinking is just an ordinary thought.

I was studying Mathematics and when i got introduced by the Pi and they said like this value of it goes on and on like forever. So the catch is that i that if that's the case if somehow we could convert those number of pi into letters it might be possible that we could find every single possible realities like everyone's name and may be their whole life time story?

And i have tried finding my name "Gaurav" G=7 A=1 U=21 R=18 A=1 V=22
i ran a python script but it failed cause it could crash my PC but still i tried and to my surprise i found it, yes, my name i found it....
...55189108068154163976 712118122 88808911934930347050...

So, my point is this be possible that our past, future and present may be all of that lies in the values of PI....(am falling in love with Mathematics hehe)

Lemme know you guys thoughts on this....!!

Long story short, I was in care as a child and now while I'm at university, the social services pay £135 of my £186 p/m rent. This year, because of the government I'm having to pay in monthly installements (as opposed to previous years where you pay a lump sum per term).

The problem is this: I can get the social services to pay their part 3 months in advance (£405). So that should cover 2 months of rent, and then by the 3rd month I'd be outstanding £72. But then I get the social services to do it again. And then when I eventually in the summer next year, I'd have to pay the last three months, right? So the question is, how long can I do this until I'd eventually have to pay?

I've tried to solve this so far by doing (744×2)-(540×3), with 744 being a total month's rent, 540 being how much the social services pay and then the other two numbers are the months. But I'm not really getting a visual sense of how long I can do this for.

I know it's fine, but what bothers me a bit about Faà di Bruno's formula is that its analytical expression is not entirely explicit in a closed way because the summation does not have clear defined limits and makes it somewhat ambiguous and leaves something to mathematical convention and I would like more to know if there is an explicit analytical expression of formula, because it would be useful to me. I don't know if it is possible or if there is some other more explicit version or another type of expression of formula that fixes that, it would be excellent for me

Finite-state automaton:

Regular expression that corresponds to finite-state automaton:

(0|1)*01(0|1)*

---

Is this true? I know a more 'precise' regex is 1*0+1(0|1)* but does the one above work?

Would a regex engine first check the occurrence of 01 and then (0|1)* or not?

I asked this question on r/mathematics and I got a bunch of answers. But I'm looking to make it without using a compass and the graph paper is not translucent, that is what is meant by no measurement.

(Is there any way to get the √2 line in such a place that a perpendicular line can be drawn exactly 1 unit i.e. coinciding somehow with the grid line. )

Had a test earlier today and got stumped by the question 6^3x = 64. For reference, this was a no calculator test, and no logarithms (technically haven't been taught them yet). I asked a bunch of friends afterwards and none of them could figure it out. I searched it up, Gemini wasn't helpful even when asked to try without logarithms, ending at an answer of 'between 1 and 0'.

Is it realistic to reach the answer of ~0.7737 without a calculator or logarithms within the time constraints of 10-15 minutes?

Edit: probably a typo or I read it wrong ;-;

So in Catching Fire, the 75th Hunger Games reaps one male and one female tribute from each of 12 districts for a total of 24. Based on what we know from a Ballad of Songbirds and Snakes, no tribute is around from before the 10th Hunger Games, so there's 64 total games to pull from.

So what are the odds that in 64 games, each district has at least one male and at least one female victor to reap?

Basically, I have 24 objects and I pull them randomly out of a bag. With replacement, what are the odds that after 64 pulls, I've gotten each object at least once?

Each standard deviation is 15 numbers above the mean if that’s what it’s talking about. For MENSA I would expect this to be more clear.

EDIT: I realize I could’ve worded this better, It seems that I am confident in my answer and am just trying to prove this graph wrong, I’m not, and I now realize that the standard deviation is indeed 15. I should’ve worded it like “The standard deviation is 2.33 and not 15, right?”.

Also, remembering high school algebra vocabulary has nothing to do with IQ.

https://www.desmos.com/calculator/6bidgwpvku

I have tried accomplishing this graphically in desmos but am interested in a better solution than a symmetrical case: https://www.desmos.com/calculator/d5ecywv34w
as it is kind of boring and doesn't look very 3D

For the spring I may be taking real analysis and topology together, as well as differential equations, a functional programming course, and physics. Is this too much or fine?

I have some proof experience and am currently taking Calc 3, linear algebra, an intro programming class, and a psych gen ed, and I have a 4.0 currently. Ive self studied to chapter 2 of baby rudin.

Hi yall, my teacher is really nice but super ass at answering emails. I want to send this here to make sure I’ve got all the info I need— I know how to do all the steps, but my issue stems from actually remembering what those steps are and often mix up methods and shit. Unfortunately I won’t have another lecture and won’t be able to attend office hours until the exam, so I can’t ask him in person.

Also, how am I supposed to prove that ak is positive? He left a note on an old test that said I need to do more beyond saying that a1(or whatever the starting value is)>0 but I’m not sure exactly what he wants and I can’t find any info on my notes about it.