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In example 1 an error is made on line 3

1/((2n-1)(2n+1)) = 1/(4n+2) - 1/(4n-2)

this is not correct, the correct answer is.

1/((2n-1)(2n+1)) = 1/(4n-2) - 1/(4n+2)

"Let ϵ>0 be given and let δϵ=ϵL. Then for all x,y∈A such that ∣x−y∣<δϵ=ϵL
then ∣f(x)−f(y)∣≤L∣x−y∣=Lδϵ=L⋅ϵL=ϵ, and so f is uniformly continuous on A. ■"
Second line should be ∣f(x)−f(y)∣≤L∣x−y∣ *<* Lδϵ=L⋅ϵL=ϵ (change from equals to strictly less)

Lipschitz Functions by , 13 Jun 2018 14:11
steph1220 (guest) 12 Jun 2018 10:21
in discussion Hidden / Per page discussions » Submitting an Error on Math Online

In the Article "Equivalence of Norms in a Finite-Dimensional Linear Space" there seems to be an error with the definition of the function f in (11). I think it should be

(1)
\begin{align} \quad f(x_1, x_2, ..., x_n) =\biggr \| \sum_{k=1}^{n} x_ke_k \biggr \| \end{align}

by steph1220 (guest), 12 Jun 2018 10:21

Thanks for catching this! It has since been fixed :D.

by , 06 Jun 2018 05:34

Thank you for catching this typo! It has been corrected!

by , 04 Jun 2018 20:23

Thank you for finding this! It has since been corrected!

by , 04 Jun 2018 20:22

Thank you for catching this! I have fixed it!

by , 04 Jun 2018 20:20

I have just added some references! I had been meaning to do this for awhile. Thanks for reminding me!

by , 04 Jun 2018 20:17

This should be fixed now! Thank you for finding this!

Zim (guest) 19 May 2018 16:04
in discussion Hidden / Per page discussions » Submitting an Error on Math Online

On the page The Implicit Function Theorem, "is defined is defined" should only be "is defined" in the following line:

Suppose that y=f(x) is a single variable real-valued function that is defined is defined implicitly such that F(x,y)=F(x,y(x))=0, and suppose that the point (a,b) lies on this curve (and so F(a,b)=0).

by Zim (guest), 19 May 2018 16:04
Zeekless (guest) 15 May 2018 09:12
in discussion Hidden / Per page discussions » Submitting an Error on Math Online

On the page "List of List of Fundamental Groups of Common Spaces"
Section: "Fundamental Groups of Less Common Spaces"
Space: The Torus Minus a Point

The mistake is that the fundamental group is written to be ZxZ, while it is actually F2 (free group with 2 generators). Note that in "The Reasoning" the group is mentioned correctly.

by Zeekless (guest), 15 May 2018 09:12
Vincent (guest) 20 Mar 2018 13:18
in discussion Hidden / Per page discussions » Submitting an Error on Math Online

The Jacobian Matrix of Differentiable Functions from Rn to Rm article of real analysis

Jacobin of line (5)

by Vincent (guest), 20 Mar 2018 13:18
Naoaki (guest) 15 Mar 2018 06:58
in discussion Hidden / Per page discussions » Submitting an Error on Math Online

name: the-ring-of-z-2z
error: the table 2 is not obey the rule that even * even = even, even * odd = even, odd * even = even, and odd * odd = odd.

by Naoaki (guest), 15 Mar 2018 06:58
Anthony (guest) 08 Mar 2018 17:51
in discussion Hidden / Per page discussions » Submitting an Error on Math Online

Not really a bug, but more of a quality of life update that I would like to see on the wikidot. I want to know what books you used to create each subsection. Keep up the great work! :D

by Anthony (guest), 08 Mar 2018 17:51

In (2), shouldn't we have

alpha is homotopic to alpha', relative to {0,1}, and
beta is homotopic to beta', relative to {0,1}

?

We did not specify any restrictions on x or y, and so the domain is

(1)
\begin{align} D(f)=\{(x,y)∈\mathbb{R}^2:x,y∈\mathbb{R}\}=\mathbb{R}^2 \end{align}

Furthermore, we know that the plane

(2)
$$z=x+y$$

has a normal vector

(3)
\begin{align} \vec{n}=(1,1,−1) \end{align}

and so this plane is not parallel to the xy-plane, and so

(4)
\begin{align} R(f)=\mathbb{R}^2 \end{align}

But, since we are talking about a two-variable input and a real, scalar (single number) output, shouldn't the Range be

(5)
\begin{align} R(f)=\mathbb{R} \end{align}

?

Functions of Several Variables by , 23 Feb 2018 14:50

Example 5:

Similar to example 4 that I have just posted; the page says the Domain is:

(1)
\begin{align} D(f)=\{(x,y):y≥x \wedge y≠x^2\} \end{align}

Shouldn't the Domain be:

(2)
\begin{align} D(f)=\{(x,y):y≥-x \wedge y≠x^2\} \end{align}

(Negative sign on x)

Example 4:

Determine and illustrate the domain of the function

(1)
$$f(x,y)=ln(x+y)$$

We note that

(2)
$$x+y>0$$

and so the domain of f contains all points

(3)
$$(x,y)$$

such that

(4)
$$y>x$$

in other words

(5)
\begin{align} D(f)=\{(x,y):y>x\} \end{align}

as depicted.

But shouldn't it be:

(6)
\begin{align} D(f)=\{(x,y):y>-x\} \end{align}

?

Guest (guest) 23 Feb 2018 07:07
in discussion Hidden / Per page discussions » Submitting an Error on Math Online

On the page "Biology Application - Population Growth Curves" in the Calculus section, there is a discrepancy in the population functions. In all cases, the function is notated as P(t) and P'(t), but both the function itself and the derivative operator are in terms of x (e.g. d/dx instead of d/dt and (-10000/x+20) vs (-10000/t+20). When finding out P'(100) when t = 100, 100 is plugged in for x instead. This could be cleared up by changing all of the x's to t's.

Keep up the good work here!

by Guest (guest), 23 Feb 2018 07:07

Thank you everyone for posting errors! I have tried to fix (most) of them!

by , 18 Feb 2018 03:45
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