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There's a typo while calculating ||r'(t)||, that is the magnitude of the tangent vector. You have written,

(1)
\begin{align} \| \vec{r'}(t) \| = \sqrt{R^2 \sin ^2 t + R^2 \cos ^2 t} = \sqrt{R^2} = R^2 \end{align}

It should be $\sqrt{R^2} = R$
obviously.

Meh (guest) 05 Dec 2017 14:52
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On the tietze-transformations page, in the example, the last line deletes the variable a, which changes the group. Instead I think the variable z should have been added first, with z=a.

by Meh (guest), 05 Dec 2017 14:52
Chaaben (guest) 29 Nov 2017 14:37
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Hi,

on the page: Properties of Adjoints of Linear Maps

Proposition 3: Proof: We note that <(T*)*(v),w> = <v,(T*)*(w)>

I think it should be: <(T*)(v),w> = <v,(T*)*(w)>

Thank you

by Chaaben (guest), 29 Nov 2017 14:37
Chaaben (guest) 28 Nov 2017 13:42
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Hi,

on the page: Eigenvalues and Eigenvectors Examples 1

In the Example 3, the converse direction of the proof: … Since[[ T^{-1}\$ is also …

Thank you

by Chaaben (guest), 28 Nov 2017 13:42
Chaaben (guest) 27 Nov 2017 19:12
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Hi,

on the page: Linear Maps

An equivalent definition … T(u+v) + T(u) + T(v) (Additivity)

I think it should be, T(u+v) = T(u) + T(v) (Additivity)

Thank you

by Chaaben (guest), 27 Nov 2017 19:12
Chaaben (guest) 27 Nov 2017 15:45
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Hi,

on the page: Range of a Linear Map

Proof of Lemma 2, the fifth point: From Lemma 1, we have that 0W = range(T).

I think it should be, 0W ∈ range(T).

Thank you

by Chaaben (guest), 27 Nov 2017 15:45
Chaaben (guest) 27 Nov 2017 14:01
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Hi,

on the page: Eigenvalues and Eigenvectors Examples 3

In Example 1: 3y = λ(λy
2)

I think it should be 3y = λ(λy)/2

Thank you

by Chaaben (guest), 27 Nov 2017 14:01
Chaaben (guest) 26 Nov 2017 10:31
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Hi,

on the page: Injective, Surjective, and Bijective Functions

At the bottom of the page: In the examples from earlier, we see that f is both injective and surjective, so g is bijective.

I think it should be, f is bijective.

Thank you

by Chaaben (guest), 26 Nov 2017 10:31
Chaaben (guest) 25 Nov 2017 13:35
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Hi,

on the page: Self-Adjoint Linear Operators

The example T(x,y)=(2x+3y,3x+2y): Note that T(1,0)=(2,3) and T(0,1)=(3,0).
So T(0,1) should be equal to (3,2).

Thank you

by Chaaben (guest), 25 Nov 2017 13:35
Chaaben (guest) 25 Nov 2017 12:30
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Hi,

on the page: Polynomials Applied to Linear Operators Examples 2

At the bottom of the page: We have that then every zero, λ1,λ2,…,λm is an eigenvalue of T.
I think it is meant, every nonzero λ1,λ2,…,λm

Thank you

by Chaaben (guest), 25 Nov 2017 12:30
Chaaben (guest) 25 Nov 2017 11:11
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Hi,

on the page: The Ring of Polynomials with Ring Coefficients

The sixth requirement: For all a, b ∈ R we have that a∗b=b∗a (Closure under ∗).
I think it should be: For all a, b ∈ R we have that a∗b ∈ R

Thank you

by Chaaben (guest), 25 Nov 2017 11:11
Sectra (guest) 24 Nov 2017 11:23
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In the "The Law of Syllogism" I think it should be: ((p->q) and (q->r)) -> (p->r)

by Sectra (guest), 24 Nov 2017 11:23
Chaaben (guest) 23 Nov 2017 10:21
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Hi,

on the Page: The Baire Category Theorem Review
On The Baire Category Theorem for Complete Metric Spaces page we … open and ##gold|dense#3 sets in X.

It is about the symbol # and the word gold.

Thank you

by Chaaben (guest), 23 Nov 2017 10:21
Krait (guest) 30 Oct 2017 17:49
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The Characterization Theorem for Intervals

I just discovered this web and it's awesome, thank you so much! I was reading the Characterization Theorem and two things sound weird to me:
-In Case 2, I believe there is a bracket missing in the 4th line: z\in[x,y
-In Case 3, I believe that inf(S) proves that S subset [a,infinity), not (a,infinity).

by Krait (guest), 30 Oct 2017 17:49

Equation (6) and preceding line: replace ' dx/dz|y i.e. partial of x with respect to z at constant y ' with
' dy/dz|w i.e. partial of y with respect to z at constant w '.

here is the mistake :
"Note that the definitions of an algebra and a σ-algebra on a set X are similar. The only difference is that an algebra on a set X is closed under finite unions, while an algebra on a set X is closed under countably infinite unions.//"

about σ-Algebras of Sets by , 27 Oct 2017 15:06
17 Oct 2017 02:40
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Hi,
Thank you for your website. I have found these typos in the page "
Bases of a Topology"

In the line after Eq. 2, it should be written as,
U is subset of P(X).

In the last line of the page, it should be written as,
Therefore every….

Thank you.
MTT

Bases of a Topology by , 17 Oct 2017 02:40
Chaaben (guest) 07 Oct 2017 16:21
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Hi,

the name of the page: Bounded Sequences of Real Numbers.

Conversely, if |an| ≤ M0 for every n ∈ N then M0 ≤ an ≤ M0 for all n ∈ N.

I think it should be: Conversely, if |an| ≤ M0 for every n ∈ N then -M0 ≤ an ≤ M0 for all n ∈ N.

The minus sign before M0 is missing.

Thank you very much.

by Chaaben (guest), 07 Oct 2017 16:21
Aaron (guest) 07 Sep 2017 05:50
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In your page "Derivative Notation", you mentioned that one limitation in "Euler's Notation" is that it is unable to express what variable differentiation is done with respect to. However, at least according to "The Differential and Integral Calculus" (1842) by Augustus De Morgan (pp. 268; a preview can be found on Google Books) the notation is modified using a subscript of the variable when it is ambiguous. This could be edited so as not to contain an unfair portrayal of the notation.

by Aaron (guest), 07 Sep 2017 05:50
Nachoo (guest) 28 Jul 2017 09:18
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Calculus - Continuity of a function - Example one:

Shouldn't it be x²+2/x if x > -2 instead of x²-2/x

Best regards and thx for making this awesome website!

by Nachoo (guest), 28 Jul 2017 09:18
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