Mathematics

Do points lie on tangents lines "only?" From: "The slope of the tangent" Or on the curve itself?? If it's not on the curve, then: Where did that curve come from?? I'm not getting the ideas behind the following. ( x + delta h) I'm very familiar with linear equations but this does not clarify tangent points and the "fancy" albegra doesn't explain the evolution of time either cuz it sets everything at 0... Are these Points Hyper Planes?? Light Cones?? Faster Than Light Speeds?? N Gons?? Oragami?? ----->Standing Waves Maybe???

One thing I notice is that many shapes in 2-space; squares, circles, etc... can all have the common word "surface" apply to them. Even non-2-space descriptions like "the Earth's surface" still refer to the kinds of things that could intersect with each other at a point, along a line, along a curve, etc... just like 2-D shapes can. It seems the word surface more generally refers to that which is either 2-dimensional or could theoretically be unfurled to FORM something 2-dimensional. (Granted, if you did that with the Earth's surface a lot of people would get hypothermia pretty quickly!) Alternatively, it seems to refer to anything which Stokes' Theorem may apply to. Are th…

Did Issac Newton know about numeral systems? IE Bases 10, 2, 1 etc etc? If not then, why do we use them "in calculus today??" Moreover, how can computers compute calculus? Issac Newton didn't have one, or did he?? Was it a Macintosh?? seriously.. This should be a very interesting thread..

Why are numbers between 0 and 1 fractions? And what base uses this "rule"? Base 10??? As in % ??? Hopefully this question doesn't receive "scrutiny" It's ok if nobody doesn't know the answer..lol

Whenever I write a sum in Latex, the limits appear forward of the sum sign. I have seen many instances where the limits are below and above. What is the code to get them there?

As conciseness is one of main mathematical features, I would like to discuss one particular instance of it. Can someone please summarize in that context the usefulness of excluding number one from the set of prime numbers? As the definition of prime numbers would be more concise without it, ie if one was included, and in fact it was at the beginning, first great contributors to number theory who laid foundations to prime number theory considered it to be prime, exclusion was introduced later, without much change in the essence of the theory, so it must have payed off somehow in terms of development of shorter expressions of consequences of somewhat longer definition, and …

Is there a mathematical way to represent the formula itself? i.e. this sentence is about itself being informative

How do we solve polynomial equations? I only know how to simplify them. If you could solve this polynomial say N = 85 it would earn a million dollars. Remember who gave it to you. x^3 = N^2 * (x^2/(N^2/x + x)) Solve for x

To start off: when we use 2pi*r = circumference.. Is 2 a coefficient? Or is it a natural number?

e.g. defining them by specific (but no more than) several criteria. 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

The Russell set formula is inconsistent. But almost every language allows for contradictory or incorrect but grammatically correct formulas. For example, the arithmetic expression 1 + 1 = 5 is incorrect and inconsistent. Thus, Russell proved not the inconsistency of set theory (Cantor's), but only that the language allows for incorrect expressions

e.g.: [math] \pi = \frac{22}{7} [/math] (only 4 operation is allowed)

So recently I was watching a movie (I'll not specify which in the interest of avoiding spoilers) where a character claims she'll curse another character's name until the day she dies, and then the character dies that same day. I know it sounds pedantic as all hell, but it got me wondering whether what she said was technically true. For the word "until" to be applicable in a discrete context, would more than one day have to be involved, or would one-day intervals also count? More generally, would "until" have to include the end date in the interval? I'm going to leave this thread open to other words as well, in case others are wondering about how other words' m…

I had previously thought that this topic would suit in physics but decided in maths, however if not, I apologise in advance. 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 val…

I am trying to analyze graphs. 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...?

how to find the complexity of a formulation ( in terms of constraints and variables) (we refer generally to the notation (o(n^2) variables and o(n^3) constraints) ( i would be grateful if you mention links or examples explaining this question) - how can we justify a large gap in execution time for two formulations of the same complexity ?

Ok, so I'm taking discrete mathematics this semester and I cannot....can not, for the life of me understand the basics of counting. I was in class an the professor was talking and everyone was agreeing and I was sitting there wondering about how many fries can go with a shake, because I saw my future and it involved flunking out of college *little bit of humor there* . Any help, any would be appreciated in understanding the concepts of counting. 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.

What does it mean to have consecutive values in set theory? How are they related

I am currently working on a GR related project, and I wonder if there is anyone here who has access to a MAPLE installation? I need help to save me lots of work with the following: suppose we have a GR spacetime endowed with the usual Levi-Civita connection and the metric \[ds^{2} =-\left( 1-\frac{2M( u)}{r}\right) du^{2} -2dudr+r^{2}\left( d\theta ^{2} +sin^{2} \theta d\phi ^{2}\right)\] 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 th…

hi, 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.

Dear maths lovers 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 v…

Can someone explain to a layman what they do, Why are they important? https://en.m.wikipedia.org/wiki/Penrose_tiling

Do most composite numbers have a large prime factor? 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, 4…

is there such a definition in the content of integral account/calculation courses or in the content of calculus? 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

I was browsing the web and I came across something which claimed to be the principle of omniscience: 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