haha, dude how is a b5#13 not a real chord? My post was a joke, but there is no such thing as a chord that isn't real.
so I chose the scale degrees 1, 3, b5, #13
e major scale = E F# G# A B C# D#
I II III IV V VI VII
A 13th is just a sixth one octave above. Just as a 9th is a second, one octave above.
Emajb5#13 would then comprise of the notes: E G# Bb C##
Of course, D is technically just a min7th, but this is all a matter of enharmonic equivalence. I am a beginner at music theory, so if someone sees that I am wrong with my analysis here please correct me.
Point is, you can take any notes, slap 'em together and get a chord. Whether they will be playable with your four fingers is another thing to consider. So no, I did not post a "fake chord".