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The reason I prefer starting at 0 is due to a computer science background and also, I think it helps to start at 0 because there are certain reasons that demand it (in particular, combinatorics) and I think having exposure to starting at 0 is 'healthier' in the long run?

Teaching both starting at 0 or 1 is probably cause for confusion for a lot of students and they usually do not have the discernment to decide which to start at.

Any advice on the issue?

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    $\begingroup$ I go with the author of the textbook I use, and I discuss this issue with the students. $\endgroup$
    – Sue VanHattum ♦
    Commented Nov 29, 2022 at 0:40
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    $\begingroup$ xkcd.com/163 $\endgroup$
    – David E Speyer
    Commented Nov 29, 2022 at 3:47
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    $\begingroup$ I would make a stronger claim: if the students struggle to understand that it does not matter whether to start indexing at 0 or 1, then you cannot teach them anything substantial about sequences anyway. $\endgroup$
    – Kostya_I
    Commented Nov 29, 2022 at 11:08
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    $\begingroup$ What age are we talking about? Little kids learn to count at 1 and aren't ready to learn to count from 0. $\endgroup$
    – Amy B
    Commented Nov 29, 2022 at 15:00
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    $\begingroup$ @RustyCore little kids in the US learn to count from their parents, books, and sesame street. All of them start with 1. Suddenly switching to 0 will confuse them. If the OP is talking about older kids then it is a different discussion. The OP hasn't specified an age. $\endgroup$
    – Amy B
    Commented Dec 1, 2022 at 7:22

1 Answer 1

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I think it is wrong to insist on one or the other. Instead, you should try to pick the one that makes the most sense. If the sequence arises from a discrete process then there should be a 0th term for the initial state. If the sequence is simply a finite tuple then it should in many cases start from a 1st term. In general, a sequence should be viewed as a function from an indexing set to a target set, so you should pick the index set that makes the most sense. Students should be taught to do that too; they should be asked to give a reason for their choice of starting from 0 or 1.

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  • $\begingroup$ "Students should be taught to do that too; they should be asked to give a reason for their choice of starting from $0$ or $1$..." or $2$, or $-5$, or $47$, or whatever. :D $\endgroup$
    – Xander Henderson ♦
    Commented Jun 26 at 14:37
  • $\begingroup$ @XanderHenderson: Of course. =) $\endgroup$
    – user21820
    Commented Jun 26 at 14:42

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