What's 0.99999... x 0.99999... ?

Well?

0.999999999999... = 1-(1/∞)
thus
0.999999999999... * 0.999999999999...
=(1-(1/∞))*(1-(1/∞))=
=1-(1/∞)-(1/∞)+(1/∞)²=
=1-(2/∞)+(1/∞)²
*** since (1/∞)² = (1/∞) ***
=1-(2/∞)+(1/∞)
=1-(1/∞)
=0.999999999999...