Here is a math question :

First I'm going to define some things (some names may already exists that I don't know of, so please take my definition into consideration)

- let's call p[n] the nth-rank prime number p[0]=1, p[1]=2, p[2]=3, p[3]=5 etc

- as you know, each integer >0 can be written as a product of integer powers of prime numbers.. let's call it the "prime writing" of a number... i'll write u[n]

so for any integer X we have

X = product( p[n] ^ u[n] )

- we can extend this to rational numbers, simply by allowing u[n] <0

My question is : can we define a set of irrational numbers in ]0 ; 1[ that extends p[n] when n<0 and are the building blocks for irrational numbers ? Let's call them subprimes..

Those numbers would have the properties following :

- they are not power/products of primes and other sub-primes and of course integer powers of some other real number (other than themselves)

Are they already known ? Do they exist ? How to construct them ?

I have some (very faint) clue :

When you elevate these numbers to positive powers , you get closer and closer to 0.. so the more you go close to 0, the more likely to find a power of a bigger subprime.. so the density must decrease closer to 0.. you get some sort of sieve, but closer and closer to 0. ]]>

https://en.wikipedia.org/wiki/Number_line

Is it possible to find points corresponding to infinitesimals on a number line? I mean finding an infinitesimal between two neighbouring points (between two real numbers).

I am assuming that every point is surrounded by neighbourhood. I got this idea of neighbouring points from John L . Bells' book A Primer of Infinitesimal Analyis (2008).

On page 6, he mentions the concept of ‘infinitesimal neighbourhood of 0’. But I think he would not consider his infinitesimals as points because on page 3 he writes

that "Since an infinitesimal in the sense just described is a part of the continuum from which it has been extracted, it follows that it cannot be a point:

to emphasize this we shall call such infinitesimals nonpunctiform."

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I was looking on the post about the reliability of published research.

And I was wondering if we could know, a posteriori, if a study is dependable or not.

Do you know any statistic test to improve our understanding of already published paper?

In biology I have seen a lot of people doing three or four different tests to see if their results are meaningful. Isn't it a kind of fraud?

Thank you very much. ]]>

\[ f''(x) = \frac{f(x+2dx) -2(f+dx) + f(x)}{(dx)^2} \]

I am using a finite difference approximation called "Second order forward" from the link, I use dx instead of h:

https://en.wikipedia.org/wiki/Finite_difference#Higher-order_differences

]]>for all ,x : if 0<x<π/2 and |x-a|<c ,then |((sqrt sinx) +1)^2-((sqrt sin a) +1)^2|<b ]]>

I read an article about infinities, and as always, I don't get it.

The writer says : "℘(ℕ)" and "ℕ" are not in bijection..

but, it seems easy to me to create a bijection :

You take the binary writing of a number, and you take the rank integer that correspond to each 1

0 <=> {}

1 <=> {0}

2 <=> {1 }

3 <=> {0 ; 1 }

4 <=> { 2 }

...

259 <=> { 0; 1 ; 8 }

..

etc and so on

you have an integer for each set of integer and vice-versa, isn't it a bijection ?

So what did I got wrong ?

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I was wondering if someone could, please, troll me about the reason why this doesn't disprove the mathematics of probabilities, since the outcome of flipping more and more coins in a row approaches closer and closer to half of the coins being heads or tails.

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Consider any total linear ordering, <*, of the reals. To make it simpler consider <* for S={x: 0<x}. At this point we don't know if <* is a well ordering or not. I will show by math induction that a well ordering of S must produce a countable number of minimums for a particular collection of subsets of S. Then I'll show all numbers, z, must be in this collection or set of minimums. Thus, the conclusion must be that if **R** can be well ordered it must be a countable set and we know this is not true.

*The above is a preliminary test before going further to make sure my topic does not get closed*

I'm a civil engineer and completed my Msc (Maths) focusing on Numerical Study 10 years ago. After my semi retirement as a result of my financial freedom, i have been studying some practical Maths problem for fun.

Recently I've been trying to model and solve a 2 digit lottery drawing game, and i failed. It's purely my imagination since i didn't see this in anywhere. But who knows it may exist?

Suppose we have a lottery game of 2 digits, drawn from 2 separate but identical electrical drums as lottery company always have. Each drum consists of 10 balls, numbered from 0 to 9, to be drawn as a pair and the drawn balls are to be replaced. In one game, 12 pairs of numbers to be drawn as winning numbers, on every Saturday and Sunday.

Eg

A particular Saturday: 09, 21, 04, 31, 48, 61, 00, 32, 99, 98, 11, 99

Sunday: another 12 pairs of numbers

My question is: if you have the result of last 1000 game, how do you calculate the most probable drawn numbers (one or two pairs) for the next drawing?

Any idea?

]]>I'm a freshman in university and I'm studying Computer science and engineering. This will be my second year of studying. We don't have Calculus as a mandatory class but I can take it from elective classes.

Is calculus necessary for my future as a student and would it help me in data science or AI? That's what I'm really interested in and I want to work for either of them. Would Calculus make my education easier in the future and in my work? In my next semesters, I want to take just Artificial intelligence and Data Science classes (Data mining, Data Science, Mechanical Learning, etc). Is calculus used there?

Thanks for your time reading and answering my question.

[math](x+5)^x=7[/math].

I know that to get I can use the Omega function Lambert W Function, however, I can't understand how it works. Thus, I ask for help of those of you who know how to solve this kind of equations (showing as much steps as you can) in order to give me reference point for further studying of this topic.

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Here is the pattern required to enumerate the reals (that is to "prove" that they are *countable*).

I don't for a moment suggest that Cantor's method is at all sensible or correct. In fact it is the most unmathematical hand-waving you could imagine.

**Commercial link removed by moderator**

Ok, I was looking for a way to apply the cantor argument to rational number (because I'm masochist) and I think I found one. I'm sure somebody will be happy to disprove my idea :

I write rational numbers in a special way. Let's say you have a/b

I decompose a and b into sums of 1s..

a= 1 + 1 + .... + 1+1+1

b= 1+ 1+ .. +1+1..

first I simplify, then I use it to create a pseudo number like this : when there's a 1 in the first line, and 1 in the second : it's 3. When 0 and 0 => 0, when 1 and 0 => 2 and when 0 and 1 => 1

So for instance

4 / 5 = > 33331000000....

12/6 = 2/1 => 3200000...

I then use it to fill a cantor-like array

now I use the diagonal to create a new row

If it's a 0, i put a 1 in the new row

If it's a 1, i put a 2 in the new row

If it's a 2, i put a 3 in the new row

If it's a 3, i put a 0 in the new row

Now we are sure that are new number is either +1 or -1 or - 1 -1 on a or b from each previous row.. So it's a new row.

(ok there may be a special case when 1+1 / 1+1 = 1/1 but we can obviously exclude 1 from rows from the beginning)

Did I just prove that Card (ℚ)> Card (ℕ) ?

a+8b+27c+64d+125e=0

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I've got this question here (more like an research assignment) which requires me to predict further values in a given set of values.

I've attached a picture for a better understanding.

The data is the cases of influenza in a country over the years.

There's values missing in from May onwards.

We have to use the previous set of data, come up with a "Prediction model" and use that to predict the values until end of 2019.

The thing is, our teacher is very incompetent, and only told us to use "polynomials from the graphs we make in excel" and use that...

Anyone got any clues/hints on how i could come up with this prediction model? Please ask if you need any of the graphs.

P.S. I used the polynomial of 6 for the graphing.

The graphing is done monthly, (Jan - December for a year) ]]>

2025, 1000, 335, 300, 187.5, 135, 99.5, 20, 17.5, and 13.5. I know that the total of all 2000 numbers is about 12,000.

What I am looking for is a recognised long tail curve model which using the first 10 numbers only predicts a total for all 2000 numbers in the sequence. I need the total to ideally be between 11,000 and 13,000. I did look at Zipfs law but I'm not sure this works.

I am not a mathematician but would appreciate any recognised models/distribution curves/laws you could suggest and what the model you suggest would give as a total for all 2000 numbers in the sequence knowing only the first 10 numbers.

The key thing that I am trying to do is fit these numbers to a recognised curve / long tail model. I am less bothered about the total (although ideally in the range 11000-13000) and more bothered about the model being something that would be recognised by mathematicians globally.

I hope this is clear. Thank you so much in advance to anyone who tries to solve this for me!

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I have been having a hard time with this equation...

I would really like to know if anybody has an idea on how to solve it...

All the suggestions are very much appreciated :)

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lets say I have coordinates for 3 points, and I want to find a function that satisfies the following

- Function pass through all the points
- Function is strictly increasing
- Function type is either: exponential, logarithmic, or involves x powers; in other words, we will omit sinusoidal functions and rational functions.

we can think of any number of points as an example.

so, lets say: point p1 = (6.5 ,1) p2 = (7.0, 2) p3=(7.48, 3)

how do I find a fitting function for these? I can easily spot that this cannot be a logarithmic function (because slope is decreasing), nor can it be in the form ax^b unliss the power is b>1 (for same reason)

but what power of X is best chosen? is it better to make it in the form Ax^b or is it better to choose multiple powers? I think multiple powers wont satisfy the strictly increasing condition.

the form C+ Ae^bx can be easily worked out I think, I guess I will give it a go in a minute

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I am trying to solve this triple integral problem , but I am having some issues.

I tried with the 2 different approaches.

1.- I converted the variables to spherical coordinates, and I think it went well, until the moment to evaluate the integral using those limits (-1 , -2). I couldn't pass that.

2.- Conversion to cylindrical coordinates, but no luck at all there.

So, could someone be so kind in giving me some light around this? Please. Not sure if I am follow a right approach.

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