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I don't believe just being transcendental is sufficient for that property.

E.g. I can't imagine that pi with all the '1' digits replaced by '2' isn't transcendental, but it clearly doesn't contain every sequence of digits.

I think you mean normal numbers.

You're right: normal, not transcendental.

IIRC, most real numbers are normal, and many important transcendental numbers are thought to be (but have not been proven to be) normal.

I edited my comment. Thank you for the correction!

> most real numbers are normal

Which means that most real numbers violate all present and future copyrights.