For instance, for a randomly generated infinite binary sequence S = 001010111010... it is well known that almost surely S has the following properties:

There are infinitely many n so that the first n digits of S consists of exactly equallymany occurences of 0 and 1. Furthermore, such n are however sparse in the sense that the density of such points of total balance is 0.

Do these properties also hold for any binary normal number? Or could we construct a binary normal number for instance where there are no such n at all? Or is it generally true that whatever property almost surely holds for a randomly generated sequence, must also hold for a normal number of same base? I couldn't figure this out myself nor find any information online.

I’ve been exploring the debate around rounding methods in statistical analysis, particularly in quartile calculations and the use of the Mendenhall-Sincich method. Chiong’s side argues that despite the method being outdated, we should still round down. On the other hand, the ‘airon side’ suggests using the normal ‘round up’ method since the Mendenhall-Sincich method is no longer in use. Both sides are compelling, but I’m inclined towards the ‘airon side.’ What are your thoughts on this debate?

I’ve been exploring the debate around rounding methods in statistical analysis, particularly in quartile calculations and the use of the Mendenhall-Sincich method. Chiong’s side argues that despite the method being outdated, we should still round down. On the other hand, the ‘airon side’ suggests using the normal ‘round up’ method since the Mendenhall-Sincich method is no longer in use. Both sides are compelling, but I’m inclined towards the ‘airon side.’ What are your thoughts on this debate?

The papers have been handed on few days ago (it is not a homework, it is just cultural) and I haven't met anyone who was able to awnser it (even after the exam, even among the best in the country). I'm really curious on if it is practically awnserable by any math student and if there exist exams that hard anywhere in the world

Question 10, Maths D (among 45 questions in 6 hours), with written in italics : Harder question

Let f be the power series expansion of a rational fraction P/Q ∈ℚ(x) with only rational poles. Suppose that the primitive ∫_0^x f(t) dt is globally bounded. Show that ∫_0^x f(t) dt is the power series development of a rational fraction in ℚ(x)

Edit : a friend found a valid proof using a simple elements decomposition...

Hello mates, if this type of question or request is not allowed here, just let me know and i'll delete, and i apologize in advance.

I am making a math mobile game, where users try to identify prime numbers, and for each diffulty i try to include different topics, as follows:

Difficulty:

• Normal: Natural numbers raging from 1-25; Numbers with addition(+) operation; Subtraction(-) operation; And Division(/) operation.
• Intelligent:
  • Natural numbers with Powers and the Operations(+; - ; /), ex: 2^3 - 9, 7^3 - 13, (16/8)^3;
  • Numbers with square roots, powers and the operations, ex: sqrt(25+8), sqrt(13^2), sqrt(81/9), 2sqrt(3^2)

Now im stuck at the Genius and Maniac Difficulty. I want to introduce Logarithms, Limits, Derivatives and Integrals.

So i need if possible:

• About 25 Logarithms Equation or other types of expression, that only use the (+) operator, you can use powers if you want, and the result of this equation or expression must be a prime number;
• I need the same but with the (-) Subtraction operator;
• And (/) Division operator;

You can add Square root, Euler number, Logarithms... Whaterver you want, go crazy, as long as the results are prime numbers.

And I will need this for Limits, Derivatives and Integrals.

I tried to come up with some equation with Logarithms, Limits, Derivatives and Integrals, but im too dumb to make something advanced or challenging for a math major, or a University professor math level... Thats why i'm here. Can you mates Help me?

Thank you for reading, and i again, apologize if this is not the place for what i'm requesting.

I found this math game called Math 24, in which you have to form 24 using 4 random numbers. If the countdown reach zero you lose. Every time you pass a level you gain 5 seconds. If you like the idea, you can try it out and tell me how it goes. My record is 79 if you're curious.

https://play.google.com/store/apps/details?id=com.mjsbest24game&pcampaignid=web_share

I'm studying set theory and related stuff independently and I need some help with this problem

Is there a set S such that S ∩ P(S) ≠ ∅ ?

I tried and here's what I did:

Let's assume that there is a set S such that, S ∩ P(S) = ∅

Now, For any set S, S ∈ P(S)

⇒ S = S ∩ P(S) = ∅

⇒ S = ∅

Which means that for any S ≠ ∅, S ∩ P(S) ≠ ∅

Is this a correct way to solve it or am I over looking something?

i need to know if this website are giving a correct solution to this operation if not, how do i solve it ?

https://preview.redd.it/5j0kj2qaawuc1.png?width=268&format=png&auto=webp&s=b317b1e3f137bcabe3fc2848d310764b3306359c

https://preview.redd.it/6wbhalx7awuc1.png?width=831&format=png&auto=webp&s=22677fd5c20cd7a5f25f4a19614f1ea9afaa67ea

Deleted and reposted cos it glitched, came up with a word problem that's worded strange to try pull people off the scent, can anyone get it? Or is it even possible?? (Pretty sure it is/s)

When x y and z are mentioned we imagine north/south as x, east/west as y & up/ down as z. A man stands on a 23.6m high cliff facing east, the sea lies at the base of it. If he were to see out of his feet, he would see a boat at a 23.8 degree depression. The ship travels north but unfortunately his ship logs were lost by the waves. :( although you manage to recover a muddled message: we took 7 nuggles south followed by 5 scampries north to correct our course.

*3 nuggles add 2 scampries is 36m *a scamprie minus 7 nuggles is -37m

We see a cloud, it is aligned with us on the x and z axis, but with the current position of the boat on the y, we walk along the x axis (along the cliff) untill we are aligned with the y axis of the boat, when we get there, their is a buetifull beach that lowers us to sea level.

How far are we from the aforementioned cloud (our feet of course)?

Give your awnser in meters and the first 4 digits, if it was 5m it would be 5000, 3.24674m=3246 782.34m=7823

Hi everyone,

I've written a little basic formula that results in 30. *but*, it will only result in 30 if I get the order of operations correct 😂. Help please? What I've got, without any parenthesis's etc is:

√900 = 30

30 - 5*3 = 15

15 / 2 = 7.5

7.5 * 3 = 22.5

22.5-20 = 2.5

2.5 * 12 = 30

Please heeeelp! I cannot math. or arithmetic. Honestly sometimes counting is outside my wheelhouse.