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In university I had to work on a project, that concerns number $3141592653589793$. Teacher told me, that since there are no zeros, I should work in $9$ based numbering system. But in $9$ based numbering system there is $0$. So is it possible to use "made up" $9$ based numbering system, which will consist from numbers from $1$ to $9$? Or is my teacher really messed up?

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    Wouldn't such a "number system" be equivalent to base $9$ representation? If such a system means real numbers, then it should include the additive identity, $0$. How you represent it depends, $0$ is just a aribtrary symbol used to denote the additive identity. – 2017-01-22
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    You could work in base $9$ where you use the symbol $1$ for $0$, $2$ for $1$, $\ldots$, $9$ for $8$. But that would be a different number than the original one in base $10$. – 2017-01-22
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    @Spenser well, it would be a different number even if I would use normal base 9. I am just affraid that this task makes no sense. – 2017-01-22
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    @newbie It makes no sense to use base $9$ for that number unless you define what the symbols $9$ in that sequence of digits mean. – 2017-01-22
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    You could equally well set $9:=0$ to have a meaningful number. But in any case, you need to choose a particular convention; there is no standard one. – 2017-01-22
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    I would suspect it was a joke. You don't want to change bases every time depending on what digits are used, so if I want the number $1234_{10}$ I should write it in base $4$? You certainly can do base $9$ with any nine different symbols for the digits, but why express your number that way? – 2017-01-22
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    That's the digits of $\pi$, isn't it? That _does_ contain $0$ if you were to continue it a bit further:$$\pi=3.141592653589 7932384626433832795 \color{Red}0288419\dots$$ – 2017-01-22
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    well I'm with you on this one, the thing is, that teacher doesn't seem to understand that part. And I doubt that any logics will work with her. So I would like to try to work on this, to show her at least something. But I'm really confused about all this stuff. – 2017-01-22

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