I know there are already many answers online to the question “why 1 is not prime”, such as https://blogs.scientificamerican.com/roots-of-unity/why-isnt-1-a-prime-number/ for example, but I didn’t find a satisfactory one.
]]>i.e. this sentence is about itself being informative
]]>
x^3 = N^2 * (x^2/(N^2/x + x))
Solve for x
]]>when we use 2pi*r = circumference..
Is 2 a coefficient?
Or is it a natural number?
]]>
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 values in domain sets are angles)
Thanks in advance.
]]>How are they related
]]>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
]]>
(only 4 operation is allowed)
]]>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.
]]>
I'm going to leave this thread open to other words as well, in case others are wondering about how other words' mathematical definitions compare/contrast with their common ones. (Although I probably will wonder about them myself.)
]]>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...?
]]>
I could go on and on, but I'll go onto explain some of the basic syntax of LaTeX.
Syntax
Functions & General Syntax
Basically put, if you want to write a math equation in LaTeX, you just write it. If you wanted f(x) = 3, then bung that between to math tags and you're done, producing [math]f(x)=3[/math]. Don't worry about extra spaces or carriage returns, because in general LaTeX will ignore them. It does get a little more complex than this, but don't worry about that for now. Remember that any letters you type in will be presumed to be some kind of variable and hence will be italicised.
We also have functions to display more complex things like matrices and fractions, and they have the syntax of having a \ before them, usually followed by some kind of argument. For example, \sin will produce the function sin and \frac{num}{denom} will produce a fraction with a specified numerator and denominator. More on these later.
Also remember that LaTeX is case sensitive, so \sigma is NOT the same as \Sigma.
Subscripts and Superscripts
This is perhaps one of the easiest things to do in LaTeX, and one of the most useful. Let's, for the sake of argument, say you wanted to write x^{2}. Then you'd write x^{2}, producing [math]x^2[/math]. Notice that you don't necessarily need the { and } in cases where you only have 1 thing in the index, for example x^2. But it does care if you want to write something like [math]x^{3x+2}[/math]. Subscripts are done similarly, but you use the _ operator instead of ^. If you want both subscript and superscript, then use the syntax x^{2}_{1} - which is equivalent to x_{1}^{2}.
Fractions and functions
As I've mentioned, fractions are generated by using the function \frac{num}{denom}. For example:
[math]\frac{1}{3}[/math]
[math]\frac{7}{x^2}[/math]
If you want smaller fractions, you can use \tfrac, to produce things like [math]\tfrac{1}{2}[/math] which will fit into a line nicely without having to seperate it.
LaTeX has some nice in-built functions like \sin, \cos, etc. I'm not going to write them all down here, but I'll point you to a website at the end of the document that contains them. Likewise, you can write symbols (such as infinity by using \infty) and Greek letters (e.g. \phi, \Sigma, \sigma, etc)
Bracketing
You can get all your usual brackets just by typing them straight in; for instance, (, |, [, etc. However, sometimes they won't be the right size, especially if you want to write something like (1/2)^{n}. You can get around this by using the \left and \right commands, and then placing your favourite brackets after them. For instance, to write (1/2)^{n}, we have:
[math]\left( \frac{1}{2} \right)^{n}[/math]
Integrals, Summations and Limits
Integrals can be produced by using \int, summations by \sum and limits by \lim. You can put limits on them all in the right places by using the normal subscript/superscript commands. For instance:
[math]\int_a^b x^2 \,dx[/math]
[math]\lim_{n\to\infty} \frac{1}{n} = 0[/math]
[math]\sum_{n=1}^{\infty}\frac{1}{n^2} = \frac{\pi^2}{6}.[/math]
Summary
There's a lot more things you can do with LaTeX, and I'll try to add to this as time goes by. Have a look at:
http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/'>http://www.maths.tcd...ns/LaTeXPrimer/ - the LaTeX primer
http://omega.albany.edu:8008/Symbols.html'>http://omega.albany....08/Symbols.html - some symbols that you might find useful.
If you have any questions about the system, send me a PM and I'll try to help
Cheers.
Much as before, the idea is that in your post, you surround equations with special characters, and MathJax will convert the contained text into an equation for you. There's two types of equation that you can typeset:
\( y=x^2 \)
. Note that we do not support $ signs as most LaTeX users would be familiar with, since this occurs too frequently in text.
\[ y = \int f(x) dx \]
, which we note is exactly what one would type in a usual LaTeX document.
For reference, the old guide is still available and has a number of useful examples for those getting started.
Finally, please note that for legacy posts, the old [math] [/math]
tags will still continue to work and these will display equations as inline. However it's likely that older posts may look different to the way that they did before.
Work out the second and third powers first (9×9×9×9×9×9×9×9×9 = 387420489.) We can therefore restate the sum as 9^{387420489}
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.
]]>Its basis is that all models developed by a human is itself a model, therefore I do not want to delve to deeply into the philosophy of the subject matter, whereas I would like for this to be an overall model of existing mathematics from beginner to expert levels all explained and viewed as a general "mapping." Showing the interconnections between all of the different mathematical concepts formed which have been agreed upon. Showing all the twists and turns, all the connections, all of the branches that lead to no where.
This is a big project, I am not blind to that. However I believe that providing an overall visual mapping of mathematics as a whole will allow for a sort of "key" for future persons, a minute or a millennia away, to quickly and easily view the processes that exist so that they themselves can go back and see the holes in their knowledge. While also quite possibly coming up with new ideas and adding to the overall mapping of the analogous "cinematics math's universe."
The goal of this project is for anyone, anywhere, at anytime to be able to learn all of mathematics in a minute. To be able to master it and contribute to it in a matter of moments.
I would also like for this to grow into something more, one in which instead of conceptualizing the concept of mathematics and guessing what exists based on a developed mental mapping, there is one that actually exists. Where you can add your own name to. Like a gigantic tree of knowledge or something.
Thank you for your time
]]>\[ds^{2} =-\left( 1-\frac{2M( u)}{r}\right) du^{2} -2dudr+r^{2}\left( d\theta ^{2} +sin^{2} \theta d\phi ^{2}\right)\]
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 this is tedious, time consuming, and error prone; MAPLE has a differential geometry module that can automate this task. Is there anyone here who might be able to run this through MAPLE for me, and post the Christoffel symbols? This would save me lots of work and time
To give a wider context, I need the Christoffel symbols so that I can write down the geodesic equations, and solve them for a purely radial free fall from rest at infinity. The above metric describes the exterior of a Vaidya black hole; I know already that the in-fall time from infinity to horizon is finite and well defined (unlike in Schwarzschild spacetime), but I need to find an explicit expression for that in-fall time in terms of the mass function M(u).
Thank you in advance
]]>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
]]>
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
]]>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 view)
Thanks in advance
]]>
Does these theorems imply that we actually cannot prove that 2+2 = 4???
Is this one of the implications of these theorems???
]]>