User blog comment:Vel!/Omega and power towers/@comment-5529393-20130418175057/@comment-25418284-20130418190239

@Deedlit: I was stalking you on MathOverflow and that's how I found your question :P

@Ikosarakt1: If we replace \(\omega\) with, say, 42:

\[42^{42 \cdot 42^{42^42}} < 42^{42^{42 \cdot 42^42}}\]

which is an equality when we use \(\omega\). The property that \(1 + \omega = \omega\) is important here.