Mathematics

To start off: when we use 2pi*r = circumference.. Is 2 a coefficient? Or is it a natural number?

I had previously thought that this topic would suit in physics but decided in maths, however if not, I apologise in advance. Question: can we describe the unit of x in sine function in centimeter? for instance sin(x) is equal to 1 cm, where x is equal to π/2 centimeter. Some external comments: This question was a part of one of projects. Unfortunately I am not good in physics in the current position although I am willing to learn it but I saw (almost) no problem regarding its mathematical side. (because in fact as we know that sine function's domain set was R and value set was [-1,1] Maybe I am again failing because here the val…

What does it mean to have consecutive values in set theory? How are they related

e.g. defining them by specific (but no more than) several criteria. for instance can we say that if we have several specific points and that implied function is passing over these points, then that would be just one specific function. Or are there such specified functions? Thanks

e.g.: [math] \pi = \frac{22}{7} [/math] (only 4 operation is allowed)

The Russell set formula is inconsistent. But almost every language allows for contradictory or incorrect but grammatically correct formulas. For example, the arithmetic expression 1 + 1 = 5 is incorrect and inconsistent. Thus, Russell proved not the inconsistency of set theory (Cantor's), but only that the language allows for incorrect expressions

hi, I do not remember whether any function given in this category has had discontinuoum point. But with one notation: [math] -\infty, \infty [/math] are accepted as points. (This is real analysis) thus if any point accepts its limit one of these points,then this is not a problem. (however, one point cannot accept both of these points as limit point ,because this will be accepted as discontinuoum) elementary functions : LAPTE L: logaritmic A: arc P: polynomic T: trygnometric E: exponential. thanks.

So recently I was watching a movie (I'll not specify which in the interest of avoiding spoilers) where a character claims she'll curse another character's name until the day she dies, and then the character dies that same day. I know it sounds pedantic as all hell, but it got me wondering whether what she said was technically true. For the word "until" to be applicable in a discrete context, would more than one day have to be involved, or would one-day intervals also count? More generally, would "until" have to include the end date in the interval? I'm going to leave this thread open to other words as well, in case others are wondering about how other words' m…

I am trying to analyze graphs. but the interesting thing is that although I change the intervals sensitively, it gives me the same graph. (embodiment: try to draw [math] f(x)= x^{3} [/math] ,select first the interval [-2,2] and [-5,5] or symmetric else differently, see what happens.) so, can we...?

how to find the complexity of a formulation ( in terms of constraints and variables) (we refer generally to the notation (o(n^2) variables and o(n^3) constraints) ( i would be grateful if you mention links or examples explaining this question) - how can we justify a large gap in execution time for two formulations of the same complexity ?

What is the largest number value in base-10 you can write with just 3 digits? No symbols and characters allowed. Hints: it's not 999 Ask someone to write the largest 3-digit number and they'll respond with 999. Logical answer, but we can go bigger. Some may get the "power" brainwave and think of 999 (99 to the power of 9), which calculates out as 99×99×99×99×99×99×99× 99×99. Even better is 999 (9 to the power of 99) which calculates out as 9×9×9×9×9×9×9 ... and so on 99 times. The correct answer, however, if you extend the idea even further ends up as... 99^9 (9 to the 9th power of 9). Work out the second and third powers first (9×9×9×9×9×9×9×9×9 = …

Ok, so I'm taking discrete mathematics this semester and I cannot....can not, for the life of me understand the basics of counting. I was in class an the professor was talking and everyone was agreeing and I was sitting there wondering about how many fries can go with a shake, because I saw my future and it involved flunking out of college *little bit of humor there* . Any help, any would be appreciated in understanding the concepts of counting. The first thing that I need help on is understanding the core principles behind the product rule and how it relates to set theory so that I can at least have some reference.

I am currently working on a GR related project, and I wonder if there is anyone here who has access to a MAPLE installation? I need help to save me lots of work with the following: suppose we have a GR spacetime endowed with the usual Levi-Civita connection and the metric \[ds^{2} =-\left( 1-\frac{2M( u)}{r}\right) du^{2} -2dudr+r^{2}\left( d\theta ^{2} +sin^{2} \theta d\phi ^{2}\right)\] wherein M(u) is an unspecified everywhere differentiable function. My task is now to find all non-vanishing Christoffel symbols (2nd kind) for this metric, in terms of the mass function M(u) and its derivatives. I could of course do this by hand with pen-and-paper, but th…

is there such a definition in the content of integral account/calculation courses or in the content of calculus? I remember something like this: [math] \int^{v(x)}_{y=u(x)} f(x,y)dy [/math] if in this integral [math]f(x,y)[/math] function ( [math] \alpha \leq x \leq \beta [/math] and [math] a \leq y \leq b [/math] ) is derivable in the D region that characterized with the given inequalites in the paranthesis,then this region would be called as "regular region" but I am not sure about the exact definition could someone provide some more context about regular region (if possible)? thanks

I was browsing the web and I came across something which claimed to be the principle of omniscience: for every function p: X → 2, ∃x ∈ X(p(x) = 0) ∨ ∀x ∈ X(p(x) = 1) I thought it looked interesting, but I can’t seem to make out just exactly how it works... is this something one can use in conjunction with absolute infinite? or is it spam... any input gladly taken. -Oliver

Dear maths lovers I need sources that classify functions/sequences or functional sequences (in broad view (wide count of examples)) ,such as; *** convergent functions / sequences *** divergent functions / sequences *** differentiable functions (>1 variables) *** differentiable functions (>2 variables) *** regular continous functions *** continuous functions *** integrable functions *** lipschitz criterion satisfied functions *** cantor theorem satisfied functions *** regular convergence (functional sequences) (note: thesis and/or books are preferred ,because the soruce(s) I look for should provide broad v…

Can someone explain to a layman what they do, Why are they important? https://en.m.wikipedia.org/wiki/Penrose_tiling

I am a layman trying to understand above theorems. This could be a stupid question. Does these theorems imply that we actually cannot prove that 2+2 = 4??? Is this one of the implications of these theorems???

Do most composite numbers have a large prime factor? First, I’ll define what I mean by a “large” prime factor. Let N be a number. If a prime factor of N is greater than the square root of N, then that factor is a large prime factor of N. As an example, 11 is a large prime factor of 22, because 11 is greater than the square root of 22, and so 22 has a large prime factor On the other hand, 3 is not a large prime factor of 12 because 3 is less than the square root of 12, and so 12 does not have a large prime factor. Below is a list of composite numbers with large prime factors: 6, 10, 14, 15, 20, 21, 22, 26, 28, 33, 34, 35, 38, 39, 42, 44, 4…

A person who can solve x2 − 92y2 = 1 in less than a year is a mathematician. Brahmagupta http://en.wikipedia.org/wiki/Brahmagupta's_formula This is mine whats yours? 1/1508996212705581.8 = 6.62692186753095e-16

Is it possible to determine a transformation matrix from just a x and y matrix and the resulted transformed matrix? Say for example you have a few points on an x and y graph. You transform these points into a matrix. Lets also say that you have another graph with x and y points and you change that into a matrix. Lets finally say that a transformation matrix exist between the first and second matrix, however you have no idea what it is. Is there a possible means of solving for that said transformation matrix. Also apologies for the slight vagueness, have some linear algebra knowledge however I need to study up on it some more in order to give more …

Hey guys, If anyone is struggling with algebra, 3Bue1Brown playlist on it is really helpful

In case of right angled triangles, C^2 = A^2 +B^2 - 2AB cos(Ψ) is shortened to C^2 = A^2 +B^2 because the cosine of the angle "Ψ" which is 90° is equal to 0. But how is its cosine equal to 0.

I remember hearing someone say "almost infinite" in this video. As someone who hasn't studied very much math, "almost infinite" sounds like nonsense. Either something ends or it doesn't, there really isn't a spectrum of unending-ness. In this video he says that ''almost infinite'' pieces of verticle lines are placed along X length. Why not infinit?

For example, Consider two shapes; a circle and rectangle. Both these shapes have same area but the perimeter of circle is less than that of rectangle. Why?