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In my discrete math textbook, the question is posed to us as $12$ modular addition $4$ in the context of $\mathbb{Z}_{10}$. As a hint, it says

"Be careful. The answer is not $6$."

I am confused by this because $ 12 + 4 = 16$ and $$ 16 \text{ mod } 10$$ is $6$, so why does the textbook say it is not $6$?

There is no formal answer provided for this question so any help on an explanation would be appreciated, or any explanation if the textbook is wrong.

Thanks!

edit: to try to improve clarity of the question

The textbook used is Mathematics a Discrete Introduction, Third Edition from Scheinerman, Section 37, page 273.

The question asks:

"In the context of $\mathbb{Z}_{10}$, please calculate: $12 \oplus 4$. [Be careful. The answer is not $6$.]"

There is no answer provided from the text or no formal explanation as to why the answer is not $6$. Am I misunderstanding the question?

N. F. Taussig
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Soph
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    Your textbook is wrong. – Cornman Oct 18 '17 at 21:39
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    You should write the exact text of your textbook. It is possible you are not reading the text precisely enough. But if you are reading it correctly, the book is wrong. – Thomas Andrews Oct 18 '17 at 21:40
  • But pedantically, $12$ and $4$ are not in $\mathbb Z/10\mathbb Z$ either, so the question is meaningless with that pedantry. @mdave16 – Thomas Andrews Oct 18 '17 at 21:41
  • it was the only way i could make the answer fit the textbook :'( @ThomasAndrews – mdave16 Oct 18 '17 at 21:42
  • It's hard to believe your text says what you claim it says. – lulu Oct 18 '17 at 21:42
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    If this isn't a typo (it's hard to believe it is), perhaps the book has somehow not yet defined numbers in modular arithmetic as equivalence classes and defines 12 and 4 with respect to the usual $\mathbb{Z}$. Then the answer would be $6+10\mathbb{Z}$. Of course sane people define numbers in modular systems immediately through equivalence classes :). – Alex R. Oct 18 '17 at 21:43
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    Does your textbook say "Be careful. The answer is not 6!"? : ) – velut luna Oct 18 '17 at 21:43
  • Please reprint what your text says exactly, with no editing . Also, give the name of the text and the page reference. – lulu Oct 18 '17 at 21:45
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    Seems to be this link : https://books.google.fr/books?id=Pc0KAAAAQBAJ&pg=PA273&lpg=PA273&dq=%22Be+careful.+The+answer+is+not+6.%22&source=bl&ots=ezrrhGj17h&sig=8GjJI71gYNevwMGQseJIGJQomf0&hl=fr&sa=X&ved=0ahUKEwjA-9zxkvvWAhWBcBoKHaOkDt4Q6AEIJzAA#v=onepage&q=%22Be%20careful.%20The%20answer%20is%20not%206.%22&f=false – zwim Oct 18 '17 at 21:47
  • The book leaves something to be desired, mixing "$=$" and "$\equiv$" willy-nilly in its explanation of modular arithmetic. So who knows what they meant. – Alex R. Oct 18 '17 at 21:52
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    @zwim Good find. Right before the exercise it says "The operations $\oplus, \ominus$, and $\otimes$ are similar to $+,-$, and $\times$, respectively, one simply operates on the integers in the usual way and the reduces modulo $n$." With this in mind, the answer appears to obviously be $6$. – lulu Oct 18 '17 at 22:02
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    More mystifyingly, these appear to be the answers from the solutions manual, and there is no solution for $12 \oplus 4$, or (strangely) for $8 \ominus 5$, though there is for $5 \ominus 8$ and $12 \otimes 5$?!?! (Maybe that isn't an official solutions manual?) – Brian Tung Oct 18 '17 at 22:16
  • Let's not downvote questions without explanation, OK? – Brian Tung Oct 18 '17 at 22:17
  • The textbook used is Mathematics a Discrete Introduction, Third Edition from Scheinerman. The question asks "In the context of ℤ10, please calculate: 12 modular addition 4. [Be careful. The answer is not 6.]" There is no answer provided from the text or no formal explanation as to why the answer is not 6. Am I misunderstanding the question? – Soph Oct 18 '17 at 23:39
  • @BrianTung Your request is strange. a) You can't control the voting behavior of other users. b) Note that it has been almost 2 hours of everyone guessing what the OP is asking about, before the OP finally commented a few minutes ago. In my opinion, downvotes as unclear and votes to close as missing context were in the right place when they were made. – Simply Beautiful Art Oct 18 '17 at 23:48
  • @Soph You should [edit] the question to include such context. It will be more noticeable this way, and may prevent some users from voting to close your question. – Simply Beautiful Art Oct 18 '17 at 23:49
  • Please read this tutorial on how to typeset mathematics on this site. – N. F. Taussig Oct 19 '17 at 00:40
  • @SimplyBeautifulArt: OK. I think a couple of hours is pretty short. The OP seemed to make some effort initially, and improved that effort over time. I tend to give OP's more time to respond, but I acknowledge that not everyone agrees. – Brian Tung Oct 19 '17 at 23:18
  • @BrianTung I too find a couple of hours pretty short, and thus I haven't made any action here. The answer has certainly improved, so I'm upvoting. – Simply Beautiful Art Oct 19 '17 at 23:20

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