system
A chat on subreddit /r/NoStupidQuestions
human
Just being infinite isn't enough - 1/3 is infinite, but it's just 0.333333333...

Being non-repeating isn't even enough. I can make a decimal that never repeats like 0.12112111211112... (the number of 1s between each 2 keeps going up), but that obviously doesn't have any binary in it at all.

What you're looking for is a *normal* number - a number where any set of digits is equally likely to appear in the decimal. Proving that a number either is or isn't normal is actually really hard - in fact, the *only* numbers that have proofs of either normality or non-normality are numbers that were specifically chosen because they'd be easy to prove. Even though nobody has managed to prove it, most mathematicians would say it's fairly likely that pi is normal, and therefore *somewhere* contains your Bee Movie Binary code - a Beenary code, perhaps.
gpt
Normal number is overkill. It containing every set of decimal digits is enough.