The duplicate thread

Question

This thread is intended to help with closure of duplicates. The main use case are situations where a first attempt at duplicate closure was not successful.¹ The creation of this thread was decided here.

Some basic rules:

• Do not use this thread for other types of closures, it is only for duplicates.
• Only use this thread if the usual means did not work. In particular, you should have cast already a vote or flag, the question already has been through the close votes review queue, and it was still not marked as duplicate.²
• Keep in mind that very short answers are automatically turned into comments. So your post should probably contain at least some brief explanation in addition to links to the duplicates. (Maybe short discussion why they are duplicates, if it is not clear that they are indeed duplicates. Or a brief explanation which of the two posts is more suitable as the duplicate target.)
• If it turns out that discussion grows long and that it is contentious whether the particular question is indeed a duplicate, the question might deserve a separate post on meta.
• After the question is closed, mark this clearly at the beginning of the post. This will help other users to see which request have already been resolved. (And if question is reopened again, this should be marked in the same place. In short, the system is the same as in the thread for reopening and undeleting.)

A more low-key way to draw attention to a possible duplicate is this chat room, which has been created for similar purposes. For example, if just one vote is missing you might consider posting there instead.

¹ Other smaller coordination-tasks related to duplicate management, such as proposals for reversals of duplicate directions, could also happen here. We'll see how things evolve.

² You can find review for a particular post - if the review is already finished - from the post timeline. Alternative ways are using this SEDE query by entering the question id. If the close votes are less than week old, it is possible that they are not in the last data dump. A more laborious alternative is to look in close votes review history, which however allows to track reviews in process. Or, just wait 24 hours after your vote; then it is very likely the post has passed review.

Answer 1

NOTE: This post is about collecting links to different posts that I think should be closed as duplicates of this post explaining the basic techniques in modular arithmetic. Before acting I recommend that you also study this thread where several relevant points were raised in the answers.

OBSERVE: Votes on this answer may not reflect the popular opinion about individual questions on the list. This is because some votes were cast when the list was shorter, and it is natural that different voters feel differently about different items on the list.

• This question is about calculating the remainder of a high power of $3$ modulo $35$ (open). [Now closed as a duplicate, reopened by a single gold-badge-user vote, and then closed again as a duplicate and later deleted.].
• This question is about calculating the last digit of a high power of $3$ (open).
• And another one about the last digit of a power of seven (open).
• This underlines what is IMNSHO wrong about the profileration of the replicas - nine more or less identical answers within half an hour from a bunch of users picking low hanging fruits (open). Anyway, some saving grace comes from the fact that the modulus differs from a power of two by one, and that can be exploited.

Answer 2

Closed

The question Help on Surjection, Injection, and Bijection basically consists of four different question, all of which have been answered on this site in the past. So it should be either closed for the reason the it contains multiple questions or as a duplicate. (I have even asked in chat which of the two possibilities is better, but I got no reply.)

I am aware that duplicate is not ideal choice, but it seemed to be less harsh on a new user and in a comment I have added an explanation that one post should not contain several questions together with link to the relevant discussion on meta.

I voted to close a duplicate. I hoped that other users will notice alternative links in comments and perhaps choose some other post as a duplicate target. (So that, ideally, after closing process the duplicate banner would contain links to some or all of the subquestions.) This did not happen, but at least the links are available in the comments and in the sidebar.

The post already has been through review queue and it has at the moment 4 close votes (as a duplicate), so one last vote is missing.

Answer 3

Closed as duplicate and then merged

The question How to find $\sum_{n=0}^{\infty}\frac{1}{2^{2^n}}$? is, as far as I can say, a duplicate of Sum of Infinite Series $1 + 1/2 + 1/4 + 1/16 + \cdots$. Still after I voted to close as a duplicate, several users voted to leave open in the review.

I have also asked in chat whether or not it should be closed - the only feedback I got was this message confirming it is a duplicate (and that merging the two questions might be a reasonable idea).

Certainly I am open also to closing the questions in the other direction. (I simply voted to close the newer question as a duplicate of the older one.)

And since I am already a making a post on meta about this pair of questions, I will also ask what you think about merging them. (Of course, merging cannot be done by regular users, so the final decision will be up to the moderators.)

Answer 4

Multiple Exponentiation in Modular Arithmetic appears to be a duplicate of How do I compute $a^b\,\bmod c$ by hand? . The second question is intended to be the abstract duplicate question for all questions on that specific topic. The first question linked was closed as a duplicate and re-opened by a user with a gold tag badge.

Answer 5

Show that if $|f(z)| \leq M |z|^n$ then $f$ is a polynomial max degree n

Clear duplicates (IMO):

• Entire function bounded by a polynomial is a polynomial
• Show that an entire function is a polynomial
• Entire function Problem
• Which entire functions satisfy $\,\lvert\,f(z)\rvert \leq \lvert z\rvert^k$?
• Show that entire function $f$ is a polynomial of degree at most $n$
• Entire function such that $\lim_{ z \to \infty} \frac{f(z)}{z^N} = 0$ then $f$ is a polynomial of degree at most $N$.

Questions that ask for something slightly more general, but (IMO) are answered by the same main duplicate post:

• if $f$ is entire and $|f(z)| \leq 1+|z|^{1/2}$, why must $f$ be constant?
• An entire function is identically zero?
• maybe maximum modulus principle $ |f(z)| \leqslant 1 + |z|^{\frac{3} {2}} \forall z$
• Show that an entire function bounded by $|z|^{10/3}$ is cubic
• Entire function bounded by polynomial of degree 3/2 must be linear.
• Holomorphic function bounded by $|z|^\frac{1}{2}$ or $|z|^\frac{3}{2}$?
• Suppose $f$ is entire and there exist constants $a, b$ such that $|f(z)| \leq a|z|+b$ for all $z \in \mathbb{C}$. Then $f$ is linear
• A property of analytic functions
• Show an entire function is constant
• Prove $f(z)$ is a polynomial if $|f(z)| \leq (1 + |z|)^n$
• Suppose $f$ is entire and $|f(z)| \leq A + B |z|^{3/2}$. Show that $f$ is a linear polynomial.
• Show that a map $f\in C^1(\mathbb{C})$ is a polynomial of a degree less or equal to $n$.
• Find all entire functions such that...
• Solution verification to complex analysis problem, prove $f$ is a polynomial.

Answer 6

Crazy old lady airplane Seat Probability Problem, with 100 passengers

The target post is above. Here are 41 duplicates. Just edit this post if you find more.

A difficult probability question about choosing seats
https://math.stackexchange.com/questions/linked/5595?lq=1

Answer 7

Crazy old lady airplane Seat probability problem, generalized to n passengers.

The target post is above. Here are duplicates. Just edit this post if you find more.

Generalize airplane problem
Seating of $n$ people with tickets into $n+k$ chairs with 1st person taking a random seat
Probability of Sitting in Correct Seat

Answer 8

Closed as duplicate

Please close this as a duplicate of this. The close-vote review is completed and still missing one vote.

Answer 9

Closed

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Please consider closing this question as a duplicate of this one. The wording are quite different, but essentially both questions ask about the relationship between two definitions of smooth manifolds which are not compatible. Close vote review is completed earlier today.

Answer 10

Closed as duplicate

I think that Verifying some trigonometric identities: $\frac{\csc\theta}{\cot\theta}-\frac{\cot\theta}{\csc\theta}=\tan\theta\sin\theta$ and Proving that $\frac{\csc\theta}{\cot\theta}-\frac{\cot\theta}{\csc\theta}=\tan\theta\sin\theta$ are duplicates. The post with more answers seems to be a reasonable duplicate target. The post already went through review without being closed. (Merging does not seem to be suitable in this case, since the newer post has an answer which also comments on the mistake made by the OP.)

Answer 11

Recommendations of first introductory books on Combinatorics for greenhorns and teenagers.

The above is the target post, already linked to many duplicates! Here are MORE duplicates. Just edit this post, if you find more. No need to seek permission to edit this post.

https://math.stackexchange.com/questions/linked/1454339?lq=1
https://math.stackexchange.com/questions/linked/15201?lq=1
Very elementary number theory and combinatorics books.
A basic Combinatorics Book
Good textbooks on combinatorics for self-study

Answer 12

Recommendations of first introductory books on Number Theory for greenhorns and teenagers.

The above is the target post, already linked to many duplicates! Here are MORE duplicates. Just edit this post, if you find more. No need to seek permission to edit this post.

What books introduce Number Theory to a Grade 11 student?
What is a good book to learn number theory?
Number theory book recommendation.
Best introductory text on elementary number theory that is concise
Number theory for a high school Calculus student?

Answer 13

The two posts have been merged

The posts $X$ is homeomorphic to $X\times X$ (TIFR GS $2014$) and What can be said about topological properties of a space $X$ that is homeomorphic to $X\times X$ $?$ are (in my opinion) duplicates of each other. They contain exactly the same question (probably from the same school or from the same type of exam), the difference between them is only in the part where the OP says what they were able to do.

I think they should be merged (I have already flagged but the flag is still pending) or at least marked as a duplicate. As far as the choice of duplicate target goes, if they are not merged then probably the newer question could be better, since the answers there are (in my opinion) a bit simpler. But otherwise there is not much of a difference between them. The post already went through close votes review.

Answer 14

The original Monty Hall problem has $\ge$ 19 duplicates.

No need to seek permission to edit any of my posts here. Just edit this, if you find more duplicates.

Answer 15

Please merge, or close as duplicates, these overabundant requests for Multivariable Calculus textbooks? Don't hesitate to add other duplicates to this post.

1. TARGET and OLDEST POST — Reference for multivariable calculus

2. Multivariable Calculus books similar to "Advanced Calculus of Several Variables" by C.H. Edwards

3. Second Text for Multivariable Calculus

4. Teaching myself multivariable calculus

5. A Book recommendation for double Integrals?

6. Recommendation of multivariable calculus books

7. A book on Vector Calculus with emphasis on geometrical intuition

8. Textbook for Multivariable and/or Vector Calculus

9. Multivariable Calculus Texts (Theoretical + Computational/Intuitive/Geometric Texts)

10. Book on Advanced Calculus