Mathematics

I want to count the reals on between 0 and 1, never mind that they're supposed to be uncountable. Let F(x) be a function that mirrors each of the digits of a number across the decimal point; that is, every digit [math]a 10^b [/math] of the original number gets converted to [math]a 10^{-b}[/math]. F(x) is its own inverse. Since F(x) has an inverse, it is a bijection. If you restrict the domain of F(x) to the natural numbers, then its range is the set of all numbers from 0 to 1 with as many digits as the natural number. 1 <--> .1 2 <--> .2 ... 10 <--> .01 11 <--> .11 ... 3256 <--> .6523 ... 1234567 <--> .7654321 ... …

Hi everybody. For a long time I kind of perceived myself as a relatively dumb person as I often had pretty big problems learning math in school - and some other subjects too. I eventually dropped the school altogether and started learning computer programming on my own (and I've learned more of it than I would've in any standard school). But, some time ago, I discovered that I'm mostly a visual-spatial learner. and my learning problems seem to (mainly) come from the fact that I have hard time with the standard linear learning style which is used in schools. I need to see the big picture of things first, I think mostly in pictures and/or associations/symbols betwee…

As we know, 3 points define a plane at XYZ, if you add another point then you create a 3D polygon. My question is that if there is a way to align the new point to the others so you can create a quad plane. The info: 3 points with XYZ coordinates (base plane) 1 point with XYZ coordinates wich have to be moved on X or Y or Z to be aligned to base plane and create a quad plane.

What do you think about the idea of a logical language like mathematics with similar structure even buts its axioms and operators are derived from natural reality or nature. Such as how you have a multiplication function such as x, times, or 2(2) you would have such a structure for conservation of energy? I know that such are derived from use of math, but such themselves or natural phenomena or physical laws about the reality around us themselves are not stand alone axioms for use in math. I think a good example in the Planck constant, or reduced Planck constant. Its pretty much an axiom and its derived from reality around us or discovered in a sense. Do you think tha…

When learning a new concept, do you prefer it to be stated simply as a set of equations, explained in English, or explained graphically? My Algebra lecturer yesterday said that he wouldn't have any diagrams in the next couple of lectures because he feared that we wouldn't get it if we jumped straight into graphical representations, but I think he might have been projecting his learning style onto everyone else there. edit grave apologies for the typo in the thread title, I'm aware of the implied hypocrisy but please be aware that Fx only spell checks <textbox>s

I realized something the other day. Almost every three-dimensional shape we know of - cube, cone, cylinder, prisms, etc - can be formed simply by extending their two-dimensional equivalents - square, circle, trapezoid, etc. - into the third dimension; in other words by being given depth. There are several that this doesn't really apply for such as the square based pyramid, but that is a combination of the square and triangular-faced cone. The sphere however is different; because technically it has no two dimensional equivalent, most would say that the circle is the 2d sphere, but in reality the circle is a 2d cylinder, since if you give a circle depth, it becomes a cy…

The australian philosopher colin leslie dean points out a simple paradox in Godels incompleteness theorem that invalidate it and makes it a complete failure extracted from his book at bottom of post Godel makes the claim that there are undecidable propositions in a formal system that dont depend upon the special nature of the formal system Quote It is reasonable therefore to make the conjecture that these axioms and rules of inference are also sufficent to decide all mathematical questions which can be formally expressed in the given systems. In what follows it will be shown .. there exist relatively simple problems of ordinary whole numbers which c…

It's not really about mathematics, but about mathematicians What bibliography style are you using in LaTeX ?

I would like to have a good book to understand markov chains and stochastic differential equations, I'm really not interested in proofs, I would prefer an emphasis on application. There's many books on the subject, I don't really know which one I should take, somebody has a suggestion ?

My understanding of math currently is somewhat limited so if this offends anyone it was not my intention. Do say functions exist like sin or cos for 4D problems? OR do such functions still apply in such dimensions with no problem? What I got this from in reading up on string theory and the 10D facet it presents. I know we have a lot of math for working 2D and 3D problems, but I guess my question is do such operators or functions exist for say 7D math problems for example, or 8D and so on.

I have 20 puzzle tables (1,2,3,…,20) that contain of 10 rows (1,2,3,…,10) each. There are numbers 1,2,3,4,… in each of every tables, which has a unique position to every rows. I am just wondering if you can help me how to find the relations between them, so the next number 351,352,353,… can be placed correctly. Here I attach the tables completely. The first one find the answer shall be rewarded US $ 70. Thank you very much for your attention. Sincerely yours, Steven Wu Bali, Indonesia. Table 1 1. 7 8 10 24 27 30 39 42 43 69 74 78 144 151 154 157 170 178 196 212 214 217 226 228 233 237 238 241 247 251 2…

This is a idea that came to me when my math teacher was stressing the point that we need to write that the sqaure root of 25 is 5 and -5, and that we must include that even when that answer can only be positive. So i was think that having the sqaure root of a number like 25 in an equation for a line would result in essentail two different lines. I don't really know if you're allowed to do something like that. For example: x^2 + 2x + 25^(1/2) So that could be either + 5 or - 5 as a constant, right? Please let me know if this makes any sense.

If you have like say for instance in assembly idiv which gives you how many times it divides and then the remainder you can of course iterate to divide two numbers all the way through (or as far as you want). What I want to do is divide a number by b*c (as opposed to what b * c actually evaluates to). You can divide a by b and then that number by c to get how many times bc goes into a but I can't figure out how to get the remainder. Like if you divide 11 by 6 you can represent it 11/(3*2). 11 / 6 = 1 remainder 5. 11/3 = 3 remainder 2. (a/b = x, r) 3 / 2 = 1 remainder 1. (x/c = x-2, r-2) So we know it divides once but we have two remainders: 1, and 2, an…

Colin leslie dean claims all views end in meaninglessness ie self-contradictory As and example of this he presents the case that Godels incompletness theorem ends in meaninglessness. And that his proof was a complete failure I present Colin leslie deans book which i downloaded of the net. What do you think of this undermining of Godel

[math]{\frac{1}{2}}+{\frac{1}{4}}+{\frac{1}{8}}+...+{\frac{1}{\infty}}=1[/math]. Now there is a theoretical lamp(Thomson's Lamp) which can instantly switch between being on and off. If it is on for half a minute, then off for a quarter of a minute, then on for an eighth of a minute, at EXACTLY one minute, is it on or off?

In every vector ressource on the net you can read that the dot product of two vectors a and b can be used to find cosine of the angle between them, like this: a.b = lal * lbl * cos angle cos angle = a.b / (lal * lbl) (lal and lbl beeing the magnitude of the vectors) Finding the dot product of a and b is done like this: a.b = (a.x * b.x + a.y * b.y) (a.x, b.y and so forth beeing the horisonal and vertical length of the vectors) What wonders me is that it doesnt say anywhere that (a.x * b.y - a.y * b.x) equals the sine of the angle, which can be a very useful information too. My question is: what is this function called? It surely isn…

I feel that I could have asked this question in either the physics or mathematics part of this forum, but as the context of my question is very general, I decided to place it here. We often talk about dimensions in different circumstances and situations describing different phenomena, both abstract and "physical". My question is there a rigorous single definition for what we call a dimension? If so what should it be? For example in physics we refer to spatial dimensions, and time as dimensions, and these seem to be because of geometric relations that unify them which are not trivial. One only needs to mention the spacetime invariant interval, or Pythagorean theorem to…

I know a little about logarithms, for example, I know that in the case of 2^3 = 8, 3 is the logarithm of 8 to base 2, or 3 = log2, but how to fractional logs work, for example, 10^1.5? I'm not mathematically literate so a simple explanation would be nice. Thanks.

Hello I'm curious about something about the function f(x) = (cos(x),sin(x)). Is it a transcendental or an algebraic curve ? It looks like an algebraic curve, but I don't know if you can have cos and sin in an algebraic curve.

I'm currently revising for a resit of my Impact of Maths module which I took this year and I found really hard, especially for a module outside my main discipline. This could explain a few of my recent posts:-p . But I have just been doing a question from the book which I am using to revise for half of the course, called Mathematical Puzzling by Tony Gardiner. The question was: "3 and 5 differ by 2 and are both prime numbers. What is the next such pair? How many such pairs are there like this?" Interestingly the 1st thing I thought of was 11 and 13:doh: . I kept looking for pairs though, and it didn't seem like there was necessarily a limit. I looked in the answe…

How can you show that [math] \sum_{k=1}^{\infty} ka_kx^{k-1}+2\sum_{k=0}^{\infty} a_kx^k = 0 [/math]

if there's a positive infinity, can there be a negative infinity?

Ok this is a bit of a strange question but this is my last place to turn. Ok High output fans or any fan really is measured by CFM (Cubic feet ,Minute) Ok now what i am interested in is how to convert a fans CFM to actual WINDSPEED MPH I am sure some variables would include the following. Size of Area, Resistance, CFM, and possibly other things. But is there a way to calculate this or is that something that is just impossible. and i would just have to build a wind tunnel and run a fan with X CFM coming out of it in a specific area and then measure windspeed. i would hope not, i would like to think that is a way to mathmatically figure it out …

I feel this is (yet another:rolleyes: )area that I need to work on and familiarise myself with in maths. I know about conic sections, what they are; hyperbolae, parabolae, ellipses etc, and I have a very rough idea but not a working memory of the formulas that can describe their functions in a Cartesian coordinate plane. In order to understand them better and to gain some personal satisfaction for myself that I do; I would like to derive the formulas. I have already looked on the Internet for something of the sort, but I don't feel I have found what I was looking for. I intend to get an elementary geometry book so I can revise my knowledge of this and other related a…

i heard a show talk about a certain technology developing in geometric progress, as opposed to exponential. i'm assuming this is rather slow progression, however what exactly is geometric progress, and how does it compare to exponential and linear progress? thanks