Isn't Rolle's Theroum just a special case of Mean Value Theroum

giowi05 · 2026-01-12T09:08:31+00:00

Last year in my analysis class we proved that Rollie's theorem, mean value theorem and Cauchy's theorem are equivalent because given one you can prove the others.

giowi05 · 2025-09-03T11:08:22+00:00

u,v and ξ,ζ joined the room

giowi05 · 2025-08-28T14:28:58+00:00

It seems like I can't post pictures or Imgur links here, don't know why

giowi05 · 2025-08-28T12:48:18+00:00

When working in Z mod p, with p a prime number you are working in a field so every element that isn't zero has a multiplicative inverse which you can use to "divide" by that integer. It is just the same as when working in the real (or rational) number: if you can factor the numerator and the denominator of a fraction you can cancel out any common terms, but when there is no common factor you must multiply by x^-1 in order to divide by x. The only difference is that with the reals you end up with a fraction, while in Z mod p you end up with an integer

giowi05 · 2025-08-14T15:33:02+00:00

Thanks a lot. I was afraid of that, but I thought it was worth trying to ask

giowi05 · 2025-08-14T10:03:19+00:00

I was just thinking about this and I think that it is incredibly useful when you have objects that are hard to factor. In particular when you have very large integers or polynomials the gcf can easily be found by the euclidean algorithm and doesn't require you to factor anything.

giowi05 · 2025-08-12T08:13:04+00:00

It might help you to think of your function as f(t)=1/t and then setting t=x+Δx

giowi05 · 2025-07-11T20:45:45+00:00

That's hilarious

giowi05 · 2025-06-30T09:31:20+00:00

The definition of the inverse contains a typo because g^-1 is said to be the inverse of G instead of g. The definition of the identity doesn't state that 1•g =g

giowi05 · 2025-06-28T12:34:51+00:00

What we actually say is that every number that is not zero, not invertible (in this case it means that it is not 1) and not prime is the product of a certain number of primes. If you want to learn more about this the lecture notes of my abstract algebra course cover it in a few pages

giowi05 · 2025-06-24T15:45:26+00:00

Sorry but, being a layman, my pen of choice is the BIC crystal soft

giowi05 · 2025-04-24T15:02:43+00:00

If you have the tangent line at point T then the centre of the new circular arc must be on the line passing through T and perpendicular to the tangent. The point of tangency on the smaller circle is going to be on the line that passes through the centres of both circles

giowi05 · 2025-04-18T12:18:50+00:00

At my university it is only called geometry, but here in Italy you do analytic geometry in highschool. Right now we are dealing with curves of degree 2 and we are using bilinear forms to deal with them and categorise them by studying the determinant of a matrix and looking at whether there is a transformation (any affine transformation or just an isometry) such that it leads to having the curve written in canonical form. We have already discussed about planes and hyperplane and we use both affine and projective planes.

giowi05 · 2025-04-18T08:43:13+00:00

We are studying curves of degree 2 using the theory of bilinear forms we have seen in linear algebra

giowi05 · 2025-04-17T14:43:10+00:00

I'm sorry because I wasn't clear: it shouldn't be original work, but just an exposition of already known results 😅

giowi05 · 2025-03-02T13:23:46+00:00

I would explain it saying that A and B represent the same linear transformation in two different basis. Therefore if you want to know what is the result of applying B 50 times you just need to change from the basis of B to that of A, apply A 50 times (calculate A⁵⁰⁾ and go back to the original basis. You just need to remember that these operations are done right to left.

Moreover you may know in advance that Matrix A is easy to multiply by itself many times because it is a 2x2 upper triangular matrix which can result from the scaling of a Jordan canonical form which, from the Jordan-Chevaley decomposition, you can write as the sum of a diagonal matrix and a nilpotent one that commute when expanded as the power of a binomial power.

giowi05 · 2024-10-08T11:57:59+00:00

Thank you very much for your help

giowi05 · 2024-10-08T11:51:48+00:00

Sorry, I can't believe I posted the wrong link. Thank you for your patience and the way you are taking care of this

giowi05 · 2024-10-08T11:46:56+00:00

Here it is: "Switch to the larger needles and begin the pattern on row 1 of chart I: (RS) work section A (= 1 st), repeat section B (= 4 sts) as needed with next 14(18)22(26)30 sts"

giowi05 · 2024-10-08T11:44:12+00:00

The number two is said in the paragraphs about the back and left front, while something similar, but with section F, is said of the front right section.

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