Textbook Problem

âa. Explain how to use the following diagram to show that ${\text{Z}}^{nonneg}\times {\text{Z}}^{nonneg}$ and ${\text{Z}}^{nonneg}$ have the same cardinality.

b. Define a function $H:{\text{Z}}^{nonneg}\times {\text{Z}}^{nonneg}\to {\text{Z}}^{nonneg}$ by the formula $H\left(m,n\right)=n+\frac{\left(m+1\right)\left(m+n+1\right)}{2}$ for all nonnegative integers m and n. Intercept the action of H geomatrically using the diagram of part (a).