A Puzzle by Midnight Math

New Puzzle
Try to imagine an irrational number between 0 and 1, represented in decimal, such that nowhere in the infinite sequence of digits does the same digit repeat twice in a row. Does such a number exist? If so, show why. If not, show why not.

Previous Puzzle

Correct Answerers
Greg Edleston
Jae Young-Park
A myriad of sillies who didn’t write in

Answer: The [little]prince lives on a spherical asteroid with a circumference of 400 paces.
Errata: Jae Young-Park solved February’s puzzle as well and was not credited in last month’s issue.
Send in your solutions (with proofs) to midnight.math@outlook.com. If you are correct, you will be given the highest of accolades: your name mentioned here, next issue.