Mathematics

I am attempting to understanding implication in mathematical logic. 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 …

Does anyone have any referencs to Oricycles ? I can't seem to find any. This is a (non Euclidian) geometrical question.

Hey whats up, 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

Hello everyone. 😃 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.

If I understand the argument correctly, it's that if you compare a set of all whole numbers to a set of all whole + half numbers, when you look at each set up to number 2, set 1 would be 1 and 2 (and 0?) and set 2 would be 1/2, 1, 1 1/2 and 2 - so set 2 has more numbers, but that's only if you look up to 2. If you look at the whole sets the size of each is infinite, so neither is bigger than the other. What am I missing here?

Sir, I have recently published a paper that reveals THE EXTREMELY PRECISE Pi:Phi CORRELATION, which is firmly premised upon Classical geometric principles. Video Link: DELETED Paper Link: DELETED

Does anyone know of any research or math records on determining when a decimal number will terminate based on the inverse of its factors? 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 multiplicatio…

So I am taking my first proofs class this semester along with an application of it in mathematical statistics and I got to say. This is pretty awesome. Why have I never seen this stuff before in my lower level mathematics courses. Like it provides general reasoning and evidence for each mathematical equation. 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 relatio…

The reason you find or take a limit is when the values cannot give you an exact answer in an equation. Then the equation can be graphed, and the limit assumes the value that the function approaches on the graph. It is an extra step that can be taken to make a graphical analysis to find an approximate answer by looking at a graph. 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, bu…

Generally a tensor may be represented as a product of vectors. 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? R…

Hi all, Forgive me if this post seems long, I tried to make it as short as possible by removing any unnecessary details, and leaving only the things needed. It would really mean so much to me if you would be able to read all of it to better understand my position, but if you're unable to read all of it, just jump to the Training Regime section. Ok, here's the thing. I'm preparing myself for the college entrance exam, and I hope that 6 months of intensive study regime will be enough time for me to pass it. I would like your opinion on it to see if there is anything I would need to change The entrance exam (July, 1st) is only 10 math-based que…

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.