Stated in Terms of Von Neumann Ordinals
The reason is that the set of all ordinal numbers carries all properties of an ordinal number and would have to be considered an ordinal number itself. Then, we can construct its successor, which is strictly greater than . However, this ordinal number must be an element of since contains all ordinal numbers, and we arrive at:
- and
Read more about this topic: Burali-Forti Paradox
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