Submitting an Error on Math Online

Welcome to the Submit an Error section of Math Online. We greatly appreciate users that submit errors found on any of our pages, as it helps improve the quality of the content we put out. With there being hundreds of pages on Math Online, it is very easy to accidentally make a mistake here or there - whether it be mathematical or just a typo.

Nevertheless, to help us fix an error as quickly as possible, we ask that you please submit the errors in the following form for organization sake. All posts made that are not about errors on a page on the site will be deleted.

**In the "post title", simply write the name of the page that has the error.****In the body of the post, describe what the error is. Be as brief as possible!**

In the page titled integer division , it says that " an integer a divides b if there exists an integer c such that ad = b"

It should be ac=b.

Administrator's Note: Thank you, this has been fixed!ReplyOptionsI believe that the diagram depicting a surjective (onto) mapping on the "Injections, Surjections, and Bijections" page contains a subtle mistake.

At first glance, this appears to fit the given definiton of surjection. But this is inconsistent with the definition of a function, given on the "Different Types of Functions" page. In particular, the aforementioned page states that a function maps every element of the domain to exactly one element in the codomain. Futhermore, the Wikipedia page on "Definition of a function" states that "Given a function f:X —> Y, the set X is the domain of f". Finally, the textbook "How to Prove It" by D. Velleman considers a relation f to be a function from A to B if for all elements in A, there exists a unique element in B such that f(a) = b.

What all of these definitions of "function" have in common is that every element of the domain gets mapped. Therefore, the mapping from A to B as depicted in the diagram above (and thus on the "Injections, Surjections, and Bijections" page) should NOT depict an element in A that isn't mapped to some element in B.

I would include an image and links in this post, but I am not allowed to because I am a "low-karma" user, presumably because I'm posting for the first time.

Administrator's Note: The image has been corrected! Once again, thank you very much for spotting this mistake!ReplyOptionsYou are absolutely correct! Thank you so much for noticing this error! I will correct the image before the end of the day :).

ReplyOptionsI believe equation (1)

is incorrect since b*y = 0 (mod b);

Shouldn't it be a*x≡c(mod b) or b*y≡c(mod a) ?

Administrator's Note: Corrected! Thank you for spotting the error!ReplyOptionsYou have very good eyes! Yes, that is correct and it should be fixed now. Thank you very much.

ReplyOptionsI believe there is a typo in Example 2 regarding the inequality involving fractions

(3).The typo is 1/n > 1/n

^{2}It should be 1/n > 1/n+2.

Administrator's Note: Corrected! Thank you for finding this mistake!ReplyOptionsYes, thank you for finding this! I think the reason I made this mistake is because I was probably changing the question up and missed deleting remnants of the previous question. I also noticed that particular question can be solved much more simpler than I originally presented it to be. As a result, I tried to simplify the explanation.

ReplyOptionsIsn't it possible to construct a nonempty subset of Z that doesn't contain a least element by constructing the set of negative integers? eg, if A = { -1, -2, -3, … } then A has a largest element but does not have a least element.

Elsewhere I have seen that the well-ordering principle holds for positive integers or for nonnegative integers, but I am not sure if it holds for all integers.

Thank you for these notes, they are very helpful!

Administrator's Note: This has been fixed!ReplyOptionsWhoops, you are absolutely right! I will correct the page name and statement right now to read "The Well-Ordering Principle of the Natural Numbers". Thank you for spotting this error.

ReplyOptionsYou list 2 as an element of the prime numbers in (1), but later in the page you also list 2 as an element of the composite numbers (3). 2 should only be prime and not composite.

Administrator's Note: Corrected! Thanks again!ReplyOptionsThanks again for spotting another mistake! This should be corrected now :).

ReplyOptionsThe closure of a set B={a} with respect to the topology {{},{b},{a,b},{b,c},{a,b,c},X} where X={a,b,c,d} is {a,d} not {a,b}.

Administrator's Note: Corrected :)!ReplyOptionsThanks for spotting this mistake! It has since been corrected.

ReplyOptionsIn the article entitled "The Well-Ordering Principle of the Natural Numbers", the set of natural numbers is denoted as a blackboard bolded Z instead of a blackboard bolded N.

Administrator's Note: Corrected :)!ReplyOptionsThanks for finding this mistake! It is now corrected!

ReplyOptionsI am going to feel so dumb when this turns out to be true, but it seems to me that the most general antiderivative of f(x)=3x

^{2}is F(x)=(3x^{3}/3) + C or just x^{3}+ C where C is any constant.Administrator's Note: Corrected :)!ReplyOptionsThank you for spotting this silly mistake! It's correct now!

ReplyOptionsHi,

Thank you for creating such an amazing page.

I would like to point out a mistake in the example on page "Increasing and Decreasing Functions"

You proved that f(x) = x^2 -ln(x) is an increasing function on (0,inf) but it's actually not.

the derivative f'(x) = 2x - 1/x and f''(x) = 2 + 1/x^2 > 0 shows that f(x) has a minimum at x0= 1/sqrt(2), f(x) is indeed decreasing on (0,x0) and increasing on (x0,inf).

Mistakes are unavoidable, but they can do nothing to make your page any less amazing, keep up the good work :). Also, it would be greatly appreciated if you can add a topic on Integral Transforms especially Laplace and Fourier transforms.

Thank you very much

Hieu

Administrator's Note: Corrected :)!ReplyOptionsThanks for spotting that mistake! I have modified the example to be on the interval $[1, \infty)$ for which $f$ is increasing!

Also, thanks for the suggestion! I'm planning to add some notes on those particular topics later this year :D!

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