Mathematics

If 1/infinity is the number that when multiplied by infinity equals 1, then the number is 1/infinity. 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.

Hi there, This 'problem' torments me since a while: Let us draw one projection of a square, and the projection is seen as a rhomboid - so, draw some arbitrary rhomboid. (Imagine a square tile that you see from a certain angle - it will become slanted and therefore distorted and seen as a series of romboids as you change the angle of view. Have in mind that distance at/from which you see it does not matter - only the angle.) Q: How to find the 2nd projection of this square, and how to draw this square (full size, seen 'en face', as if seen directly under 90°)? See the image below. Milos P. S. You can rotate the image by 90 deg or change th…

So this parody of an old video game portrays a (fictional!) oil explosion on an island from a distance; and the resulting duration of silence before the noise. Obviously, if we were directly given the angle to one end of the island and angle to another we could use geometry to estimate this fictional island's length. But here we're only given the distance to the island (via sound delay) and the fraction the island takes up of the field of view. This got me wondering whether or not "field of view" can be used to estimate "range of angles" between the point of observation and the object being observed. For instance, is there a function relating what fraction of …

#1 If you have a sphere with an axis through it around which it rotates, is the number of possible axis it can have finite or infinite? #2 This is maybe the same question in a different way, but what's got me confused is this: Is the number of possible positions (for a point) on a finite line finite or infinite? Because the way I'm thinking about it, you can take a point and put it a certain distance from one end of the line and then you half the distance and get another position and you half it again and again... you get the idea, you can half it an infinite number of times, which seems to give an infinite number of positions on a finite line. So how can t…

If 0^0=1, then 0^-1 equals (0^0)/(0^1)=1/0 and 0^1=(0^0)*(0^1)=1*0=0 Therefore (1/0)*(0)=0/0 which does not equal just 1. Showing our original assumption that 0^0 equals 1, and only 1 is a fallacy.

Greetings everyone, This is my very first post here, and it comes out of pure curiosity. I see that the OP's argument draws from Russel's paradox. However, I'm having a very hard time "imagining" a set of all sets that is not a member of itself. On the contrary, I can perfectly imagine a set of all cats (like a big balloon filled with cats, for instance). The challenge for me is that Russel's paradox is an abstract mathematical concept, and I am not able to imagine anything physical out of it. Quoting the OP, "...from the very conceivable idea that you can group whatever you want together." Again, although grouping things is conceiveable for me, a s…

Hello, I wanted to present something so I could see where I went wrong. So when I was calculating the area of a circle I wanted to get a better understanding of the circumference of a circle so I found the equation for it online. ( y = sqrt(r^2 - x^2)) now this equation is for a semi-circle, but I can multiply it by 2 in order to get the full circle. so when I substituted the y term with the circumference / 2 and the x term with the diameter I got the following, ( C / 2 ) = sqrt(r^2 - (D)^2) from here you can replaced the diameter term with it radius counterpart (C / 2) = sqrt(r^2 - (2*r)^2) from this you could, in turn, combin…

So, NOT a mathematician here, not even close, just to get that out of the way. I was involved in a discussion on another board about making assumptions about causation based solely on correlations. I mentioned the well known and documented phrase that “correlation does not imply causation” and linked a couple articles to it. One person came back with something else and I have unfortunately lost the link he referenced but I remember that it led me to another article on Bayesian statistics which I thought, at the time, was related. I’m sorry I haven’t been able to locate the original reference. So, I’m not sure what to think since I don’t really understand what I’ve be…

Let's say you're graphing some function... for simplicity's sake, some quantity over time. There's a time interval that needs to be skipped because nothing happens during that time interval. What would be the proper way to skip that interval on the x-axis? I've seen zig-zags, dotted lines, etc... and I would like to be filled in on what is the correct way. Thank you in advance.

What is infinity+i, infinity i+1 and infinity i+infinity? i being the square root of -1 - the imaginary unit.

It can be shown that as x approaches 0 from the right side, 1/x will approach 1/0 and apporach positive infinity. And it can be shown that as -x approaches 0 from the left side, -1/x will approach negative infinity and apporach -1/0, which is equal to (-1/-1)*-1/0 equals 1/0, since 0 is neither positive or negative. Showing that 1/0 is not even a number, and does not represent a distinct point on the real number line.

Hello i am designing a tattoo similar to this one for someone but just want to make sure im correct in my analysis. Can someone help me out and break down the values / formulas in this tattoo and what they symbolize or represent. much appreciated. Photo attached.

I'm trying to understand what it means to take a number \(n \) to the power of \( i \). \[ F(x) = x^i = x^{\sqrt{-1}} \] I'm trying to understand visually what taking a number to a squareroot really does to it. Examine the behavior. I want to be able to understand it visually as well as numerically. I suppose it would be useful to also understand what a number \( n \) to a root \( \sqrt{a} \) also means. \[ G(y) = n ^ { \sqrt{y}} , y \in \mathbb{Z} \]

Solve for x in the below: x2= 16x Systematic procedure required if possible, please.

Solve for x in the below: \ ( x⋏2 = 16⋏x \) Systematic procedure required if possible, please.

The rays of the sun that hit the planet Earth are parallel, we know that. Even ancient Greek Eratosthenes knew that because he used this particularity for measuring the Earth's radius. Then the question arises: why at the sunset do we see the sun rays converging towards the sun? (it is a sequel of an old thread I cannot find back)

How to get an equation of a line of point (0-3) and (4,1) Can anyone help me please

I was just wondering if it is already known which two numbers can both add AND multiply to equal an arbitrary number? For example, if I choose any number, x, can you tell me what two numbers can both add AND multiply to equal x? A very easy x would be 4. 2+2=4 2×2=4 In that case, a and b are the same number, 2, but what if I told you that x has to be included. Can you satisfy the following equality: 4+4=4 AND 4×4=4 Obviously those are not true, but what transform could you do to the left hand sides, without changing the right hand sides. Simply put, how could you make 4+4 turn into 2+2 and 4×4 turn into 2×2, using the number …

I don't know much about the mathematics of chance but hear this out. What is the chance of this... You are using a message board with say, 20 other active users and 100 inactive anonymous users. All of the users are located within free countries... U.S., Canada, Europe, Australia, etc Nobody uses their photo. Nobody has identified themselves openly on the message board. And then one user posts a topic with a real photo of himself as his avatar. Another user sees that photo and thirty minutes later, at his place of work, somebody walks in who looks exactly and precisely like the person in that photo. Would you say this was a coinci…

I have a series of 3d points in space they are on an arbitrary plane but i want to move them to a plane AX+BY+CZ+D=0 A=0, B=0, C=1, D=0 so the XY Plane.the matrices for this is identity.From the points i assume 0) All vectors will be unitized1) the first point in the polygon will be moved to 0,0,02) the first and second point in the polygon will define the vector for the X Axis3) the first point and the last point in the polygon will define a construction vector4) the cross product of the X Axis Vector and the construction vector will define the Z Axis vector5) the cross product of the X Axis Vector and the Z Axis Vector will define the Y Axis Vector6) using the three vec…

is the world a graphic function in 3 dimensional cordinate system or a infinite convergent series ?

Ok I wanted to see if this idea had any potential and I figured if it didn’t it would be shot down in a matter of minutes. This is my final work on the Prime product problem. I know it is just x^2 * y^2 = PNP^2 However the terms would just cancel out. Instead I have decided to let x^2 equal a pattern of x and PNP. So I just substituted the equation which is more complex and will not equal the right side of the equation for x^2. In calculus where you have a complex derivative where you let du/dx equal a portion of the derivative so you can understand and simplify the manipulation of the integral. I am instead taking a more complex pattern and leaving it so …

So I am not sure if it was that I was applying the formula found on Wikipedia incorrectly, (if so hahaha) https://en.wikipedia.org/wiki/Summation but I developed a formula based off several similar ideas that, so far, has proven to work for all consecutive positive integers, I have not begun testing whether it is accurate with negative integers, or complex numbers (Though I would imagine that it would work with complex numbers because you calculate those very similarly to integers, but you follow special rules for them when they have exponentation etc.) \usepackage{asmmath}\displaymath:\[\sum_k^n=((n-k)+1)(\frac{n-k}{2}+k)\] As there is almost certainly a…

To start I will say to explain as a start. Lets say you have a boss and he tells you to turn off and on a lamp an infinity amount of times for a hour. This is impossible . By lets say you divide the hour by 2 that means you turn it on a 30, then after that 45, than after that 52, than so on and so on. This is impossible to find the value of when the lamp is on or off. Now to explain why infinity is a false value. You see if we put a value in to anything with infinity there is a infant amount of outcomes but there is one thing that makes infinity a false value. Thanks to one man infinity is number that can never be used. Sir Isaac Newton. His law of matter that stat…