Does these theorems imply that we actually cannot prove that 2+2 = 4???
Is this one of the implications of these theorems???
]]>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
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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.
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, 46, 51, 52, 55, 57, 58, 62, 65, 66, 68, 69, 74, …
It seems that, as numbers increase, a greater and greater percentage of them have large prime factors. I say that that seems to be true, because I have sampled some groups of big numbers, and most of them had large prime factors. Of course, that isn’t proof and as far as I know it could also be wrong.
If we check all of the numbers up to 330, the majority of counting numbers are composite numbers with large prime factors.
If I understand it correctly, then what I’m asking about is similar to the question answered by the Prime Number Theorem. According to the Prime Number Theorem, for a very large number N, the probability that a random integer not greater than N is prime is equal to 1/log(N).
Because the prime numbers are distributed in this way, and 1/log(N) can be arbitrarily close to zero, the composite numbers can be seen as essentially the same as all integers, for very large values of N. For very large numbers, my question is the same as asking what percentage of all integers have a large prime factor.
My question is, “For a very large number N, what is the probability that a random integer less than N has a large prime factor?” “Is this probability greater than 0.5?” I’m hoping there might be some kind of answer to this in the same way that the Prime Number Theorem answers the question about the distribution of prime numbers.
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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
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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
]]>
Brahmagupta
http://en.wikipedia.org/wiki/Brahmagupta's_formula
This is mine whats yours?
1/1508996212705581.8 = 6.62692186753095e-16
]]>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 concrete terms.
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If anyone is struggling with algebra, 3Bue1Brown playlist on it is really helpful
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Both these shapes have same area but the perimeter of circle is less than that of rectangle. Why?
]]>I will start off by giving an example of its use and my interpretation of how to correctly under it. That way my process can be critiqued and corrected.
Example
if "f(a) =f(a')", then " a = a' "
Interpretation
the given logical statement above is like an "instruction manual" in which if I have f(some a) = f(some b) then it will always result in some a equaling some a'.
And if I observe a counter example to this then that would mean that the overall example statement is wrong and therefore it is not defined as being that said thing, in this case
being the definition of a one to one function.
That being said if I have the function
f = {(1, a), (2, a), (3, b)} and I do some searching I find that f(1) = f(2). Because of this I can use the above example logical statement.
if f(1) = f(2), then 1 = 2. However this is not the case and therefore the initial statement is thereby false and thus it is not a one to one function.
Is this interpretation correct?
Also is this "instructional following" a good method of interpretation mathematical logic?
Thank you for your future answers.
]]>I can't seem to find any.
This is a (non Euclidian) geometrical question.
]]>question,
Is there some underlying linear understanding for how one may go about understanding mathematical proofs?
for example
Definitions -> Postulates -> Theorems -> Proofs -> etc.
Like is there a universal path of understanding for some logical statement?
The reason I ask is because when reading a little of "Journey into Mathematics" and the Elements it would continuously go through this process like one thing is built on top of another. That is cool and all but is there like an existing quantifiable formula for this process?
Thank you for your time
]]>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.
In honor of Pi Day I'm going to be explaining the very beginning of set theory (which I consider the beginning of university math) live on Twitch in about two hours (1 PM GMT).
For those who do not know Twitch, it's a completely free streaming platform - you can come in and watch without registering or anything.
Starting university math can often be confusing so I'm hoping to be of some help to people with this.
You can find the stream here:
advertising link removed by moderator per rule 2.7
Anyone and everyone is welcome to join in. 😊
Hope to see you there, and good luck with your studies,
Fluxistence.
What am I missing here?
]]>Video Link: DELETED
Paper Link: DELETED
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Yes I know that I would be working with whole numbers not integers. But for integers what if you took the factors of a quotient, say circumference divided by diameter and factored the numerator and denominator. The equation would be = to itself, but if you multiplied the factors together you already know that those factors terminate at the product.
Someone has probably done a similar technique. But factoring large numbers is recursive and then you add to the process recursion again to do the multiplication and you get a problem you can’t solve.
Also can someone explain the process that was used when they solved Pi to a trillion digits and don’t know where it stops. The stopping point is what I would describe by the multiplication of the factors. The factors multiplied together still equal the original number, but the product determines where the factors stop.
Hope this makes sense.
]]>I am currently reading over "Journey into mathematics-an introduction to proofs" by Joseph J. Rotman and it answer ssooooo many questions. Like a proof for that cosine equation that was just given to me. I thought it involved like some super human levels of mathematics. It turns out it just uses the pythagean theorem and some geometry identification and relationship forming.
Also I am reading "The Elements" by Euclid for class as well, picked it up because it looked kind of cool when I was younger and it turns out I needed it later on, nice coincidence. Turns out it is now my favorite book. Like a book that you do not want to pick up because you know you will not be able to put it down.
Like my biggest issue in my math classes was that I did not understand how the conclusion was reached.
Like omg, this is the most I have learned in a long time.
(source: Family guy)
(reason for use: for dramatic comedic appeal )
Is this what math is? finding patterns and relationships in order to develop unique structures in order to better understand the interworks of different behaviors being observed?
]]>You can say that it is a certain value, even though the calculation of the variables in the equation cannot give you an answer. It is another way of trying to deal with infinity or infinitesimals in of itself. The main reason why this method isn't used in a lot of work is because it is not known if it has been proven to be reliable, but it has been proven to be reliable when finding the derivative. Limits can potentially give false values, presumably. I have never seen any evidence of that.
]]>A “reducing tensor” may be represented as the average of vector triple products. A reducing tensor will also “reduce” to an average of scalar products.
Acceleration may be represented as a vector. A field (gravitational, electric, or magnetic) may be represented using “reducing tensors” of acceleration.
An “equivalent EFE” may be written as reducing tensors. The equivalent EFE will then reduce to scalar products of acceleration. Suitable definitions of acceleration will give the Schwarzschild metric. Christoffel symbols are not required.
Is a “reducing tensor” mathematically valid?
Reference; http://newstuff77.weebly.com 02 The Reducing Tensor
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To arrive at you would multiply (infinity)*(1/infinity)=infinity/infinity which does technically equal 1, but it does also technically equal 2 or and any other positive real. There 1/infinity should be treated as undefined.
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