1

by definition $$A^3= A \times A \times A$$ is the set of 3-tuple

and $$ A \times B = \left\{ {\left( {a,b} \right) \mid a \in A \text{ and } b \in B} \right\}. $$

so does this mean $$A \times A^2 $$ is the set of pairs of $$(a, (b, c))$$ or $$(a, b, c)$$ where $$a, b,c \in A$$

Asaf Karagila
  • 393,674
Ibrahim Abou Elenein
  • 47
  • 1
    This can help you https://math.stackexchange.com/questions/1103753/how-tot-start-proving-a-times-b-times-c-ne-a-times-b-times-c?rq=1 – Zaragosa Oct 24 '21 at 20:22
  • 1
    The answer is that $A^2 \times A$ is not the same set as $A^3$, as explained in Zaragosa's link. – Elchanan Solomon Oct 24 '21 at 20:28
  • 5
    It depends on how exactly $A^3$ is defined whether $A^3 = A^2 \times A$. However, it is definitely the case that there’s a natural bijection between them. – Mark Saving Oct 24 '21 at 20:31

0 Answers0