Analysis and Calculus

Hello, my name is Grayson. I am a bit ahead of myself, learning calculus. I understood like, 70 percent of it but I need help with integrals. My "Calculus for dummies book" Isn't explaining things good enough for me. So can anyone give me a step-by-step guide on how to solve integrals and what the best graphing calculator to use is. Because I don't have a ti-84 and all the online ones work drastically different.

Lets say there is there is two lines. Each pointing an infinitesimal rate at each other. So imagine one at -00000000...etc1 and one at 000000000...etc1. Would the lines be parallel or perpendicular?

When you perform the expression n! (read "n factorial"), you multiply all the positive integers between one and n. They have to be positive, so n>0, but they also have to be integers, so you would think that factorial of a decimal is impossible. However, when I put it into my computer's calculator, I do get a real answer. For example, .01! = 0.99432585119150603713532988870511..., and 2.1! = 2.1976202783924770541835645379483..., so there must be a way to perform a factorial of a decimal. What is it? How do you do that?

What is difference between a gradient and a derivative?

What is limited in fractions or and functions?

I want to start learning calculus(for free time along with starting it for my degree), but I want to make sure I would have a somewhat smooth time understanding it.

what doe f(x)dx mean and how is it used?

What is calculus?

For all n rows, this would be a list of all sets of natural numbers that increase by 1 starting from 1. 1 {1} 2 {1, 2} 3 {1, 2, 3} 4 {1, 2, 3, 4} . . . n Every set listed here would have to be finite since every natural number is finite. But if every possible set of increasing natural numbers (that increase by 1 starting from 1) is here, then how can the set of all natural numbers N be infinite?

What is the purpose of cosecant, secant and cotangent since you can use sine, cosine and cotangent to find sides in a right angled triangle? If it is so.

The real numbers cannot have a next number, but I don't understand how that can be logical. For example, consider the segment inclusively from 1 to 2, so there are the numbers 1 and 2 at each end of the segment. We can take off a number like 1.3 or 2 from it. If we take the number 2 away, we are left with something like the segment 1 to the limit 2 - 1/x as x goes to infinity (or whatever it is). So my ultimate question is, why can we take off the end of the segment if it is something that we call 2, but we can't take off another number? The segment only has real numbers; what makes 2 so special that it can end a segment and be removable?

I have some questions here, which I’m hoping someone might be able to help with. I’ve spent the last few years focussing on other things in my life, so I’m afraid I’ve lost touch with the some of the basics - I’ve recently attempted to once again put pen to paper and actually work out some GR tensor calculus practice problems from scratch by hand, and…let’s just say it didn’t go so well 😕 1. Notational question - assume we are working in the context of GR, ie we are on a semi-Riemannian manifold endowed with the Levi-Civita connection and a metric. What is the actual significance of the vertical alignment (or lack thereof) of indices on tensors and spinors? In other …

Especially talk of infinities are mental constructs with no physical proof that they exist. Cantor proves the Reals are uncountable by constructing an infinite list of reals paired to a natural number. Such a list can be constructed conceptually in mind, but it cannot be physically produced to check that it exits. This is why I say mathematics is a Fairy Tale.

In this paper (see attached, last hint on the page included): "theta < kappa" means "theta is equivalent to <kappa" because "|P(theta)| = 2theta <= |H(kappa)|". Is this wrong?

I've read a paper wherein there is a definition and formula amounting to "there exist some y an element of the Empty Set". This is nonsensical because Empty Set = {x: x not= x}. there is no "y not= y".

I saw in a writing: ~p -> p = false. This can't be true since 0 -> 1 = 1, so ~p -> p = p!

The Sequent Calculus has introduction and elimination rules that reflects Hilbert style axioms.

We have the Banach-Tarski paradox that says: 1 sphere = 2 spheres or 1 = 2. Since it can also be proven that 1 ~= 2, we have an inconsistency. Actually it says a sphere is equidecomposable into 2 spheres. It is then follows that: 1 = 2. To exclude this we have to make the following operation invalid: fill a hole in a line by shifting the line up to infinity.

A text says that to prove a formula A we have to refute GA (which must reduce to the negation of A). It says that for each sub-formula of the form B OR C to include the following clauses in GA: {xB OR C, ~xB}, {xB OR C, ~xC}, {xB, xC, ~xB OR C}. Shouldn't there be two ~xB OR C's and one xB OR C? As stated it resolves to xB OR C and not it's negation. If not, why not?

I have recently been studying double integrals. One of the topics were double variable substitutions. I find it hard to find the right double variable substitutions. For example: I substituted y = 1/2(u+v) and x = u+v, in hopes of getting rid of (2y-x)^3/2 and making the integral easier. However, this led me down a very long process and ended up being too complicated for it to work. Any advice?

Hello, I have been stuck on this Math problem and wanted some help. This is the formula for finding out the surface area: Using this formula, you should arrive on something like this (the outer limits are pi/4 and 0, the program didn't let me input). Focusing on the inner integral, by rearranging you arrive on this If you integrate this, the answer will always be zero: The answer to this always has to be zero, because inputting the limits inside the square root would give zero. However, if you switched to polar coordinates, you'd arrive on a different answer: Which would …

In Logic we can distinguish wrong from right definitions: "A -> B defined = ~A OR B" is right, while "A -> B defined = A OR ~B" is wrong. Other definitions are similar such as definitions according to De Morgan's Law. Now I wonder if the same applies to Mathematics?

Wikipedia says elliptic curves has complex numbers w0 and w1 such that for all z: f(z+w0) = f(z) and f(z+w1)=f(z), but y^2 = x^3 + Ax + B is not periodic so what is the real period of an Elliptic Curve?

Hello, I have a question from a book called Models of mind by Grace Lindsay Here the writer talks about the difference between biologists and mathematicians and I couldn't get the point here: Biologists study living things that are abundant with specific traits and nuanced exceptions to any rule. Mathematicians – driven by simplicity, elegance and the need to make things manageable – squash that abundance when they put it into equations.

If you have for a proposition P: P AND P -> ~P you can't conclude ~P. The premises is a contradiction.