مجموعه متعدی (نظریه مجموعه‌ها)
مثال

با استفاده از تعریف اعداد ترتیبی پیشنهاد شده توسط جان فون نویمان، اعداد ترتیبی به عنوان مجموعه‌های موروثاَ گذرا تعریف می‌شوند: یک عدد ترتیبی یک مجموعه گذرا ست که اعضایش هم گذرا (و در نتیجه عدد ترتیبی) هستند. رده از همه اعداد ترتیبی یک کلاس گذرا است.
هر یک از مراحل Vα و Lα که منجر به ساخت جهان فون نویمان V و جهان ساختنی گودل L منجر می‌شوند، مجموعه‌های گذرا هستند. جهان‌های L و V خودشان کلاس‌های گذرایند.
این یک فهرست کامل از تمام مجموعه‌های گذرا تا ۲۰ براکت است:
\{\},
\{\{\}\},
\{\{\},\{\{\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\}\},
\{\{\},\{\{\}\},\{\{\},\{\{\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\}\},\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\},\{\{\}\}\}\},\{\{\},\{\{\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\}\},\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\},\{\{\}\}\},\{\{\},\{\{\},\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\},\{\{\}\}\},\{\{\{\}\},\{\{\},\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\}\}\},\{\{\},\{\{\}\}\}\},
\{\{\},\{\{\}\},\{\{\},\{\{\}\}\},\{\{\},\{\{\}\},\{\{\},\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\}\}\},\{\{\{\{\{\}\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\}\}\},\{\{\},\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\},\{\{\}\}\}\},\{\{\},\{\{\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\}\}\},\{\{\},\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\}\}\},\{\{\},\{\{\{\{\}\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\}\}\},\{\{\{\}\},\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\}\}\},\{\{\},\{\{\},\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\}\}\},\{\{\{\}\},\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\}\}\},\{\{\{\}\},\{\{\{\{\}\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\}\}\},\{\{\},\{\{\}\},\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\},\{\{\{\}\}\}\}\},\{\{\},\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\}\}\},\{\{\{\}\},\{\{\},\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\}\}\},\{\{\},\{\{\}\},\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\{\}\}\}\},\{\{\{\}\},\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\}\}\},\{\{\{\{\}\}\},\{\{\{\{\}\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\}\}\},\{\{\},\{\{\}\},\{\{\{\{\}\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\}\}\},\{\{\{\{\}\}\},\{\{\},\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\}\}\},\{\{\},\{\{\}\},\{\{\},\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\{\}\}\}\},\{\{\},\{\{\},\{\{\{\}\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\{\}\}\}\},\{\{\},\{\{\}\},\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\{\},\{\{\}\}\}\}\},\{\{\{\},\{\{\}\}\}\},\{\{\},\{\{\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\},\{\{\}\}\}\},\{\{\},\{\{\}\}\},\{\{\},\{\{\},\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\}\}\},\{\{\},\{\{\{\}\}\},\{\{\{\{\}\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\},\{\{\{\}\}\}\}\},\{\{\{\}\},\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\}\}\},\{\{\},\{\{\{\}\}\},\{\{\},\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\},\{\{\{\}\}\}\},\{\{\{\}\},\{\{\},\{\{\{\}\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\}\},\{\{\{\}\}\}\},\{\{\},\{\{\}\},\{\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\},\{\{\}\}\}\},\{\{\},\{\{\}\}\},\{\{\},\{\{\{\},\{\{\}\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\},\{\{\}\}\}\},\{\{\},\{\{\}\}\},\{\{\{\}\},\{\{\},\{\{\}\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\}\}\},\{\{\{\{\{\}\}\}\}\},\{\{\},\{\{\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\}\}\},\{\{\{\},\{\{\}\}\}\},\{\{\},\{\{\}\}\}\},
\{\{\},\{\{\}\},\{\{\{\}\}\},\{\{\{\{\}\}\}\},\{\{\},\{\{\}\}\},\{\{\},\{\{\{\}\}\}\}\}.