Alternativität is a weakening of the associative law.

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the linkage · means alternative, if the two statements standing down apply:

  • o · (o · p) = (o · o) · p


  • o · (p · p) = (o · p) · p.


is associative a linkage, can one the clips in three and multielement expressions omit:

  • (o · q) · p = o · (q · p) = o · q · p

applies the associative law no longer, must remain standing all clips. If the Alternativität applies, one can omit the clips at least if o=q or if q=p. In particular same factors can be combined into powers. That is, that it is possible products of the kind(A · A) · ((A · A) · b) to summarize too <math> a^4 \ cdot b </math> .


see also


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