User blog comment:I am a McCree God/Millillionbulls/@comment-32783837-20180116045051/@comment-34434829-20180124184015

That's the genral idea.

Keep in mind that ordinary powers *are* defined for nonintegers. So the number (10↑)987,654,321124,586,603,628.93471... is a perfectly well-defined transcendental number. It's also a very big number, on the order of 10^^987654323.

If we call this large number N, then the next step is to do 10↑↑N.

Formally, this cannot be done without extending tetration to the reals.

Practically, since floor(N) has about 10^^987654322 digits, it doesn't matter. We'll need to calculate the top number (124,586,603,628.93471...) to about 10^^987654322 significant digits for the fractional part of N to become relevant.

To make it 100% formal, you can pick any one of the existing suggestions for extending tetration to the reals. You can even invent one yourself. As long as it obeys the reasonable rule of 10↑↑floor(N)<=10↑↑N<10↑↑floor(N+1), it will have a negligible effect on the final result.