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Nachoo (guest) 28 Jul 2017 09:18
in discussion Hidden / Per page discussions » Submitting an Error on Math Online

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

It should fit on the page a little nicer now!

And thank you for the very kind words! Glad you enjoy the site :D!

by MathOnlineMathOnline, 04 Jul 2017 03:14

Great catch! Should be fixed now! Thank you!

by MathOnlineMathOnline, 04 Jul 2017 03:10

This has been corrected!

And thank you for the kind words and for helping to find all of these typos/mistakes! I'm really glad you enjoy it :D!

Re: Vector Value Functions by MathOnlineMathOnline, 04 Jul 2017 03:02

This has been fixed! Thanks!

Re: Unit Vectors by MathOnlineMathOnline, 04 Jul 2017 02:59

Thanks! This has been fixed!

Actually the link was broken! Thank you so much for spotting this!

It's actually intentional! The first is linked under the Calculus hub page while the second is linked under the Real Analysis hub page.

The reason is that the Calculus version assumes less of the reader and is much more detailed, while the Real Analysis version is a bit briefer. In fact, there's a good chance that there's even a third version, haha :P!

Corrected! Thank you!

I'm really glad you're enjoying the website! You're right to be skeptical of the statement and the proof though!

The "Squeeze Theorem" has a few variations. The general version for sequences is that if $(a_n)$, $(b_n)$, and $(c_n)$ are sequences of real numbers and there exists some number $M$ such that $a_n \leq b_n \leq c_n$, for all $n \geq M$ and if $(a_n)$ and $(c_n)$ converge to $L$ then $(b_n)$ must also converge to $L$.

Some texts and teachers give the simpler (less general) version where it is assumed that $a_n \leq b_n \leq c_n$ for every $n$. (The same conclusion holds).

I stated the more general version but proved the simpler version. Thank you for spotting this little error! I will correct it immediately.

Corrected! Thank you!

by MathOnlineMathOnline, 04 Jul 2017 02:33

Proof that Convergent Sequences are Bounded

mathonline.wikidot. com/proof-that-convergent-sequences-are-bounded

The Boundedness of Convergent Sequences Theorem

mathonline.wikidot. com/the-boundedness-of-convergent-sequences-theorem

There are two typos where it displays "−epsilon" instead of "−ϵ".

Also another question. In the Theorem it says "an≤bn≤cn is true always after some nth term". But later in the proof you assume that this is true for all n>=N with N:=max{N1,N2}. How do you know that this chosen N is now bigger than "some nth term"? Couldn't it be smaller, so the inequality is not true yet, so the proof doesn't work?

Btw thanks a lot for this wonderful website. You helped me out a ton already!

Harold (guest) 17 Jun 2017 05:06
in discussion Hidden / Per page discussions » Submitting an Error on Math Online

Very minor typo on page titled "Invertibility of a Linear Map" under Linear Algebra subject.

It says:
"Now we only need to show that S is a linear map, that is show that S∈(W,V)."

It should be:
"Now we only need to show that S is a linear map, that is show that S∈L(W,V)."

by Harold (guest), 17 Jun 2017 05:06

Never mind, the original is correct, the limit is taken as x goes to zero.

I believe example three should result in "x + 1/ln3" as the x never cancels out with anything in the denominator.

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