Inspired from this question

Create a mathematic rule, so every integer can be written in only 1 symbol.

Note : white spaces (space, tab, etc) is considered as different symbol


closed as unclear what you're asking by Rand al'Thor, Marius, IAmInPLS, Beastly Gerbil, Alconja Sep 11 '16 at 11:52

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  • 1
    $\begingroup$ Soooo you're asking for a bijection between the sets N and Z. $\endgroup$ – Ben Frankel Sep 11 '16 at 5:15
  • $\begingroup$ I could write every integer using a dotty font. Only one symbol is used — the dots. $\endgroup$ – Shuri2060 Sep 11 '16 at 13:32
  • $\begingroup$ Kind of unary I think then???? $\endgroup$ – EKons Sep 12 '16 at 5:01

$\triangle \to 0$
$\triangle\triangle \to 1$
$\triangle\triangle\triangle \to -1$
$\triangle\triangle\triangle\triangle \to 2$
$\triangle\triangle\triangle\triangle\triangle \to -2$
$\triangle\triangle\triangle\triangle\triangle\triangle \to 3$
$\triangle\triangle\triangle\triangle\triangle\triangle\triangle \to -3$
$\triangle\triangle\triangle\triangle\triangle\triangle\triangle\triangle \to 4$
$\triangle\triangle\triangle\triangle\triangle\triangle\triangle\triangle\triangle \to -4$

  • $\begingroup$ How it works: $△$ is $0$. For other integers, if $n_△ mod 2=0$, then $n=n_△/2$. If $n_△ mod 2=1$, then the result is $n=-\lfloor n_△/2\rfloor$. $\endgroup$ – EKons Sep 12 '16 at 5:04
  • $\begingroup$ @ΈρικΚωνσταντόπουλος Or $n=(-1)^{n_△}\lfloor n_△/2\rfloor$, if you are lazy :) $\endgroup$ – Lynn Sep 12 '16 at 12:19

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