Stated another way, no one disputes that pi includes every number that has a finite representation. Thus pi includes itself in all of its increasingly precise representations, without limit, and therefore pi contains pi itself within a vanishingly small margin of error.
== Strings Numeric series without termination ==
Pi has no termination in its digital representation, no patterns in the digits, and no repetitive periodicity. Pi containing pi can be viewed as two strings: the original pi without termination in its digital representation, and another pi that starts within pi but also without any termination point.