Does It Perpetually Hold?

\[ \begin{array} {r c r c l } 0.1 &\times & 0.1 & = &0.01 \\ 0.11 & \times& 0.11 & = &0.012\ldots \\
0.111 & \times& 0.111 & =& 0.0123\ldots \\
& & & \vdots& \\
0.\underbrace{1111\ldots1}_{\text{nine }9\text{'s}} & \times&
0.\underbrace{1111\ldots1}_{\text{nine }9\text{'s}} & =& 0.0123456789\ldots \\ 0.\underbrace{1111\ldots1}_{\text{ten }9\text{'s}} & \times&
0.\underbrace{1111\ldots1}_{\text{ten }9\text{'s}} & =& 0.012345678910\ldots \\ \end{array} \]

Exactly how many of the equations above are true?


Inspiration.

×

Problem Loading...

Note Loading...

Set Loading...